: 


■        ■ 


THE 


NMl  Constructor 


GVS1MP50N;M4.N.A. 


~ '"■■'  '■'."■      ."■    ":-;~   !  IP-  <r?,°*"" 


The  D.  Van  Nostrand  Company 

intend  this  book  to  be  sold  to  the  Public 
at  the  advertised  price,  and  supply  it  to 
the  Trade  on  terms  which  will  not  allow 
of  discount. 


1 


THE 


Naval  Constructor: 

A    Vade    Mecum 

OF 

SHIP  DESIGN  FOR  STUDENTS,  NAVAL  ARCHI- 
TECTS,  SHIPBUILDERS    AND    OWNERS, 
MARINE  SUPERINTENDENTS,  ENGI- 
NEERS AND   DRAUGHTSMEN. 

BY 

GEORGE   SIMPSON, 

3IEMBEK  OF   THE   INSTITUTION   OF   NAVAL  ARCHITECTS 


NEW   YORK. 
1).   VAX  NOSTRAND  COMPANY. 

LONDON. 

KEGAN  PAUL,  TRENCH,  TRUBNER  &  CO.,  Lti>. 

DRYDEN   HOUSE,  43  GERRARD  ST. 
1904. 


Va/k 


ENGINEERING  LIBRARY 

Copyright,  1904, 

BY 

D.  VAN  NOSTRAND  COMPANY 


P  K  E  F  A  C  E. 


This  handbook  lias  been  prepared  with  the  object 
of  supplying  a  ready  reference  for  those  engaged  in  the 
design,  construction,  or  maintenance  of  ships,  —  such  a 
work  as  should  give  simply  and  concisely,  information 
on  most  of  the  points  usually  dealt  with  in  the  theory 
and  practice  of  marine  architecture,  and  in  addition 
much  that  is  new  and  original.  Under  the  latter  head- 
ing should  be  included  the  chapter  on  Design  and 
many  of  the  tables  of  standardized  fitting  details,  etc. 

The  Freeboard  tables  have  been  explained  and  their 
application  simplified  by  working  out  examples  embrac- 
ing the  various  types  to  which  freeboards  are  assigned, 
including  the  modern  shelter  decker,  for  which  rules 
have  recently  been  issued. 

While  it  would  have  been  possible  to  enlarge  greatly 
on  what  the  author  has  attempted,  it  has  been  deemed 
prudent  at  present  to  restrict  somewhat  the  scope  of 
the  book,  although  at  that,  it  will  be  found  much  more 
comprehensive  in  its  character  than  existing  works  on 
naval  architecture. 

It  has  been  the  author's  aim  to  eliminate  all  obsolete 
matter  and  antiquated  data,  and  to  bring  the  book  right 
in  line  with  present  day  requirements. 

How  nearly  he  has  come  to  this  ideal  will  be  shown 
by  the  reception  accorded  by  the  profession. 

His  thanks  are  especially  due  to  Ernest  H.  Rigg, 
A.  Bi.  I.  X.  A.,  for  valuable  assistance  in  the  prepara- 
tion of  the  chapter  on  Freeboard,  to  Jas.  A.  Thomson, 
M.  L  N.  A.,  for  aid  in  the  reading  of  proofs,  and  to 
the  publishers  for  their  hearty  co-operation. 

83(>4f>0GE0RGE    SIMPSON. 

047  Eta  hmovd  Terrace,  Mariner  Harbor, 
Nbw  York  Citt,  May,  1004. 


CONTENTS. 


Section  I.  —  Ship  Calculations. 

Symbols  —  Algebraical  Signs  —  Displacement  —  Simpson's 
First  Rule  —  Multipliers  for  Subdivided  Intervals  —  Proof  of  Simp- 
son's Rule  —  Displacement  Sections  —  Bottom  Half-breadth  —  Dis- 
placement Table  —  Area  of  Water  Plane  —  Tons  per  Inch 
Immersion  —  Coefficient  —  Immersion  Passing  from  Salt  to  Fresh 
Water  —  Area  of  Midship  Section  —  Coefficient  /3  —  Prismatic 
Coefficient  —  Centre  of  Buoyancy  — Approximate  Rule  for  Cen- 
tre of  Buoyancy  —  Centre  of  Buoyancy  Longitudinally  —  Trans- 
verse Metacentre  —  B.  M.  —  Moment  of  Inertia  of  Water  Plane  — 
Longitudinal  Metacentre  —  Centre  of  Flotation  —  Approximate 
Rule  for  L.B.M.  —  Moment  to  Change  Trim  —  Change  of  Trim  — 
Moment  to  Alter  Trim  One  Inch  —  Approximate  Rule  for  M.  — 
Alteration  in  Trim  through  shipping  a  small  weight  —  Tchiby- 
scheff's  Sections  for  "  Lucania  "  —  Displacement  Sheet  by  Tchiby- 
scheff's  Rule — Centre  of  Buoyancy  by  Tchibyscheff's  Rule  — 
L.M.C.  and  Centre  of  Flotation  by  Tchibyscheff's  Rule  —  Trans- 
verse Metacentres  by  Tchibyscheff's  Rule —  Effect  of  Form,  of 
Water  Line  on  Position  of  Longitudinal  Metacentre  — Effect  of 
Form  of  Water  Line  on  Position  of  Transverse  Metacentre  —  Ex- 
planation of  Tables  on  Position  of  Metacentres  —  Stability  Calcu- 
lation by  Tchibyscheff's  Rule  —  Tchibyscheff's  Sections  for  Sta- 
bility Levers —  Calculation  of  G.Z.  by  Tchibyscheff's  Rule  — 
Cross  Curves  of  Stability  —  Stability  Curves — Design  —  Block 
Coefficient  —  Relation  Coefficient  e  —  Mid  Area  Coefficient  /8  — 
Prismatic  Coefficient  —  Area  of  L.W.L.  Coefficient  a — Inertia 
Coefficient  "i" — Centre  of  Gravity  Coefficient  "g"  —  Bilge 
Diagonal  Coefficient  — Element  Coefficient  —  Relation  of  the  Co- 
efficients to  one  another  — Element  Coefficients  for  various  Types 

—  Coefficients  for  Centre  of  Gravity  —  Moment  of  Inertia  of 
Waterline  Coefficient  —  Sheer  —  Contour  of  Stern  —  Figureheads 
and  Lacing  Pieces —  Rail  Half-breadths — Load  Line  Half-breadths 

—  Diagram  of  Bilge  Diagonals — Diagram  of  L.W.L.  Half-breadths 

—  Body  Plan  of  "Oceanic" — Designing  the  Bossing  —  Fairing 
the  Bossing  —  Fairing  the  Oxter  —  Elements  of  Marine  Engines  — 

ii 


Contents  iii 


Engine  Room  Lengths  —  The  Preparation  of  Specifications 

—  Specification  Headings  — Freeboard  — Coefficient  of  Fineness 

—  Dimensions  for  Freeboards  —  Sheer  for  Freeboard —  Round  of 
Beam  (Freeboard)  —  Standard  Freeing  Fort  Area  —  Types  of  Ves- 
sels (Freeboard)  —  Flush  Deck  Vessel  —  Monkey  Forecastle  — 
Bridge  Honse  —  Steering  Gear  Hood  —  Topgallant  Forecastle  — 
Poop  —  Raised  Quarter  Deck  —  Well  Decked  Vessel  —  Shade 
Decked  Vessel  —  Awning   Decked  Vessel  —  Spar  Decked  Vessel 

—  Turret  Deck  Vessel —  Trunk  Deck  Vessel  —  Freeboard  Ta- 
bles —  Freeboards  for  Freighters  —  Freeboards  for  Spar  Deckers 

—  Freeboards  for  Awning  Deckers  —  Notes  on  Freeboard  Tables 

—  Correction  for  Variations  —  Deductions  for  Erections  —  Ex- 
amples of  Freeboard  —  Freeboard  for  Shelter  Deckers  — Ton- 
nage Openings  —  Freeboard  Marks  —  Statutory  Deck  Line  — 
Load  Draught  Diagrams  —  Kirk's  Analysis  —  Analysis  Data 

—  Wetted  Surface  Formula  —  Launching  —  Launching  Periods 

—  Launching  Curves  —  Camber  of  Ways  — Declivity  of  Ways  — 
Pressure  on  Dog  Shores  —  Length  of  Ways  —  Tables  of  Launch- 
ing Data  —  Calculation  of  Hull  Weights  —  Ditto  by  Johnson's 
Method  —  Johnson's  Curves  —  Complete  Tables  of  Weights  of 
Steel  Shapes  —  The  Transport  of  Cattle  —  Arrangement  of 
Stalls  and  Pens  —  Dimensions  of  Stalls  and  Pens  —  Board 
of  Agriculture  Regulations —  Detailed  Weights  of  Cattle  Fittings 

—  Rudder  Formulae  —  Spectacle  Frames  —  Proportions  of 
Spectacle  Frames — Propeller  Struts  —  Simpson's  Formula  for 
Propeller  Struts  —  Proportions  of  Brackets  —  Centre  of  Gravity 
by  Experiment  —  Centre  of  Gravity  by  Calculation.  —  Strength 
of  Ships  —  Hogging  —  Sagging  —  Curve  of  Weights  —  Curve  of 
Buoyancy  —  Curve  of  Loads  —  Curve  of  Shearing  Stresses  — 
Curve  of  Bending  Moments  —  Specimen  Calculations  for 
Moments  of  Inertia  —  Diagram  of  Strength  Curves  —  Re- 
sistance of  Ships  —  The  Admiralty  Constant  —  Table  of  Con- 
stants for  various  Types  —  Froude's  Investigations  —  Law  of 
Comparison  — Application  of  Froude's  Law  —  Speed  and  Power 
Curve  —  Standard  Curves  of  Power  —  I.H.P.  by  Independent 
Method  —  Skin  Resistance — Residuary  Resistance  Power  — 
Form  of  Least  Resistance  —  Middendorf's  Method  —  Table  of 
Angles  of  Entrance  and  Run  —  Table  of  Steamers'  Data. 


Section  II.  —  Strength  of  Materials. 

Strength   of  Materials  —  Ultimate  Strength  —  Working   Load 

—  Proof  Strength  —  Stress  and  Strain  —  Tensile  Stress—  Compres- 
sive Stress —  Shearing  Stress  — Bending  Stress  —  Torsional  Stress 

—  Resilience  —  Elasticity  —  Modulus  of  Elasticity  —  Permanent  Set 


iv  Contents 

—  Moment  of  Inertia  —  Neutral  Surface  —  Section  Modulus  — 
Moment  of  Resistance  —  Kadius  of  Gyration  —  Various  Stresses 
and  their  Factors  —  Elements  of  Sections  —  Beam  Bending 
Moments  —  Elements  of  Circular  Sections  —  Moment  of  Inertia 
of  Circular  Sections  —  Strength  of  Columns  —  Johnson's  Formula 
for  Columns  —  Least  Radius  of  Gyration  for  various  Sections 

—  Values  for  Johnson's  Formula  —  Pipe  Pillars — Standard  Pipe 
Elements  —  Steel  Columns  —  Strength  of  Metals  and  Alloys  — 
Physical  Properties  of  Timber  —  Strength  of  Timber  —  Weight 
and  Strength  of  Wire  Rope  —  Notes  on  the  Use  of  Wire  Rope  — 
Strength  of  Chain  Cables  —  Proof  Load  for  Chains  —  Strength 
of  Guard  Chains  —  Weight  of  Chain  Cables  —  Breaking  Strength 
of  Chains  —  Elements  of  Angles  —  Elements  of  Bulb  Angles  — 
Elements  of  Deck  Beams  —  Elements  of  Tees  —  Elements  of 
2  bars  —  Tees  as  Struts  —  Bending  Moments  of  Pins  —  Strength 
of  Special  Shackles  —  Riveting  U.  S.  Navy  —  Standard  Rivets  — 
Lloyd's  Riveting  Table  —  Tables  of  Strength  of  Riveting  — 
Ordered  Lengths  of  Rivets  —  Shearing  and  Bearing  Tables  of 
Rivets. 

Section  III. — Fittings  and  Details. 

Structural  Details —  Keels  —  Bar  Keel  —  Keel  Scarphs  —  Tack 
Rivets  in  Keels  —  Universal  Bar  —  Flat  Plate  Keels  —  Centre 
Keelson  —  Keel  Doublings  —  Stems  —  Stern  Frames  —  Braces  — 
Gudgeons  —  Pintles  —  Riveting  of  Boss  —  Rudder  Post  —  Body 
Post  —  Rudders  —  Single  Plate  Rudder  —  Norman  Head  —  Rud- 
der Arms  —  Coupling  Palm  —  Coupling  Bolts — Rudder  Stock  — 
Cast  Steel  Rudder  —  Balanced  Rudders  —  Heel  Bearing  —  Emer- 
gency Chains  —  Types  of  Rudder  Carriers  —  Rudder  Trunks  — 
Tail  Plates  —  Propeller  Struts  —  Area  of  Propeller  Brackets  — 
Boss  Barrel  —  Spectacle  Frames  —  Bossing  around  Shafts  — 
Tube-end  Castings  —  Framing—  Resistance  of  Frames  —  Cut 
Frames  — Pressed  Plate  Chocks  —  Stapled  Collars  —  Frame  Doub- 
lings —  Spirketting  Plate  —  Framing  of  Superstructure —  Reverse 
Frames  —  Floors — Stresses  on  Floors  —  Flanged  Floors  —  Chan- 
nel Floors  —  Water-tight  Floors  —  Floor  Brackets  —  End  Floors 

—  Inner  Bottoms  —  Water-tight  Compartments — Centre  Vertical 
Girder — Side  Girders  —  Margin  Plate  —  Ceiling  on  Tanks  — 
Bitumastic  Cement  —  Manholes  —  Tank  Bleeders  —  Beams  — 
Beam  Camber  —  Welded  Beam  Knees  —  Bracket  Knees  —  Stan- 
dard Beam  Knees  —  Strong  Beams  —  Carlings — Deck  Girders  — 
Beam  Collars  —  Hold  Pillars  —  Built  Columns  —  Pipe  Pillars  — 
Standard  Solid  Heads  and  Heels  —  Fitting  of  Pillars —  Heels  on 
Inner  Bottoms  — Staggered  Pillars  —  Hatches  —  Size  of  Hatches 

—  Hatch  Corner  Doublings  —  Corner  Angles  —  Hatch  Fore  and 


Contents 


Afters  —  Bridle  Beams — Standard  Hatch  Cleats  —  Battening 
Bar  —  Hatch  Wedges —  Hatch  Ledges —  Hatch  Lashing  Kings  — 
Hatch  Covers  — Lifting  Rings  —  Web  Frames —  Keelsons  —  In- 
tercostal Plates — Side  Stringers  —  Bulkhead  Collars— Longitudi- 
nals —  Ending  of  Keelsons  —  Bulkheads  —  Collision  Bulkheads 

—  Bulkhead  Liners  —  Bottom  Plating  Bhd.  —  Stiffeners  —  Stresses 
on  Bulkheads  —  Deep  Framing  —  Caulking  —  Chafing  Pieces  — 
Shell  Plating—  Arrangement  of  Strakes  —  Plate  Lines—  Fairing 
the  Lines  on  Model  —  Shift  of  Butts—  Furnaced  Plates  —  Land- 
ings —  Butts  of  Plating  —  Garboard  Strake  —  Sheerstrake  —  Shell 
Riveting— Stealers— Jogging — Scarphs  of  Overlaps — Liners  at 
Overlaps  —  Scarphing  of  Landing  Edges  on  Stem  and  Stern  Post 

—  Holes  through  Shell  —  Doubling  Plates — Hood  End  Plates  — 
Doublings  at  Breaks—  Fitting  Details  —  The  Preparation  of  De- 
tails —  Standardizing  Details  —  Bill  of  Material  —  Standard  Hatch- 
ing—Graphic Division  of  One  Inch  —  Baldt  Anchors  —  Ingle- 
field  Anchors  —  Hall  Anchors  —  Admiral  Anchors  —  Anchor 
Cranes  —  Stress  on  Anchor  Cranes — Dimensions  of  Anchor 
Cranes— Ship's  Bells— Weight  of  Bells  — Belay  Pins  — Stan- 
dard Bollards — Weights  of  Bollards — Standard  Iron  Blocks  — 
U.  S.  Standard  Bolts  and  Nuts  — Cast  Steel  Cleats  — Catting 
Hooks  —  Crane  Hooks  —  Weights  of  Boats  and  Davit  Diameters 

—  Standard  Hinged  W.  T.  Doors  —  Standard  Sliding  W.  T. 
Doors  —  Details  of  W.  T.  Doors  —  Standard  Eyebolts  —  Stan- 
dard Fairleads  —  Weight  of  Fairleads— Flanges  for  Lead 
Pipes  —  Standard  Pipe  Flanges  —  Standard  Flanges  for  Venti- 
lation —  Standard  Hand  Wheels  (Iron)  —  Standard  Hand  Wheels 
(Brass)  —  Hawse  Pipe   Proportions —  Weights  of  Hawse  Pipes 

—  Keys  and  Key  ways  —  Plug  Cock  Keys  —  Standard  Pad  Eyes  — 
Wrought  Iron  Rings  —  Ring  Plates  —  Dimensions  of  Wood 
Screws — Areas  of  Sea  Anchors  —  Detail  of  Sea  Anchor  — 
Trade  Shackles — Standard   Shackles —  Standard  Worked  Eyes 

—  Towing  Bitts  —  Weights  of  Sidelights  —  Proportions  of  Chain 
Slips  —  Stuffing  Boxes  and  Glands — Thimbles  for  Wire  Rope  — 
Standard  Toggle  Pins — Admiralty  Turnbuckles  —  Weight  of 
Cowls  —  Standard   Ventilating  Cowls. 

Section  IV. — Rigging  and  Ropes. 

Standing  Rigging —  Table  of  Wire  Rope  —  Splices  —  Thimbles 

—  Sheaves  —  Turnbuckles  —  Running  Rigging  —  Manila  —  Hemp 

—  Coir  —  Blocks  —  Tackles  —  Power  gained  by  Blocks  —  Whip  — 
Double  Whip  —  Guntackle  Purchase  —  Burton  —  Double  Spanish 
Burton  —  Luff  Tackle  —  Rigging  Derricks. 


vi  Contents 


Section  V.  —  Equipment. 

Anchors  and  Chains  —  Lloyd's  Equipment  —  Lloyd's  Table  — 
Hawsers  and  Warps  —  Tables  of  Equipment  —  Weights  —  Boats 
—  Notes  on  Construction —  Diagram  of  Proportions  —  Lifeboats  — 
Cutters  —  Dinghies  —  Gigs  —  Barges  —  Galleys  —  Table  of  Scant- 
lings for  Rowboats —  Sail  Area  —  Drawing  of  Standard  Lifeboat 
in  Detail  —  Lifting  Rings  and  Slings  —  Board  of  Trade  Require- 
ments—  Supervising  Inspector's  Requirements  —  Sea  Anchors  — 
Axes,  Buckets,  etc.  — Light  Screens  —  Tonnage  —  Various  Ton- 
nage Rules— Y.  R.  A.  and  N.  Y.  Y.  C.  Rules  —  Windlasses  — 
Towing  Machines,  etc. 

Section  VI.  —  Miscellaneous. 

Tables    of   Weights  —  Measures  —  Outfits  —  Materials  —  etc.  — 

ptr>  etc. 

Section  VII. —Tables. 

Complete  mathematical  tables  specially  arranged. 


SYMBOLS     COMMON     IN    NAVAL    ARCHI- 
TECTURE    USED    IN    THIS    BOOK. 


A  .  . 
S.A.  . 
C.E. 


a  . 

b  . 
Bm 
Bx 
Bid 

0. 

B     . 
C.B. 

G  . 

C.G. 
H  . 
D  . 
V  . 
D  + 
D- 
Z>-^ 
-<-D 

8- 
c  . 
F 
Fr 

9- 

A.P, 
F.P. 

X  • 


y.a 


Area  of  load  water  plane. 
Sail  area  in  square  feet. 
Centre  of  effort  of  sail  plan. 

Distance  of  centre  of  effort  forward  of  centre  of  im- 
mersed lateral  plane. 

Coefficient  of  fineness  of  load  water  line  —  ■= =r- 

Li  X   H 

Bilge  diagonal  coefficient. 
Moulded  breadth  of  ship. 
Extreme  breadth  of  ship. 
Water-line  breadth  of  ship. 

Coefficient  of  midship  section  area  = 

B  x  a 

Centre  of  gravity  of  displacement  (centre  of  buoyancy). 
Centre  of  gravity  of  displacement  from   aft  perpen- 
dicular. 
Centre  of  gravity  of  ship  above  base. 
Centre  of  gravity  of  ship  and  engines. 
Moulded  depth  to  upper  deck. 
Displacement  in  tons  of  salt  water  (gross). 
Displacement  in  cubic  feet  (volume). 
Displacement  in  tons  at  load  draught. 
Displacement  in  tons  at  light. 
Displacement  of  fore  body. 
Displacement  of  after  body. 

Coefficient  of  fineness  of  displacement  (block  coefficient). 
Relation  coefficient. 
Freeboard  from  statutory  deck  line. 
Freeboard  to  top  of  rail  amidship. 

Q 

Coefficient  of  centre  of  gravity  =  -=• 

After  perpendicular  (after  side  of  rudder  post). 
Forward  perpendicular  (fore  side  of  stem  at  upper  deck). 
Indicates  the  half-length  lift  ween  perpendiculars  and  is 
the  sign  of  the  mid  section  or  "dead  flat." 

vii 


M.C. 
G.Z.  . 
G.M. 
B.M. 

L.M.C. 

~G  . 

j£  • 

P    • 

I.H.P. 

E.H.P. 

N.P. 

B.P. 

W.L. 

wl  . 

O.A. 

R    . 

I.  . 

M  . 
M" 

0    . 

o  • 

© 
<8> 


y-  . 

JO  •     • 

w.s. 

B    . 
1<2,  or 
d.  . 

d->- 
-<-d 

■e-. 
p  . 

V  . 

C    . 


u, 


The   Naval   Constructor 


Mid-section  area. 

Height  of  transverse  metacentre  above  base. 
Stability  lever. 

Height  of  transverse  metacentre  above  centre  of  gravity. 
Height  of  transverse  metacentre  above  centre  of  buoy- 
ancy. 
Longitudinal  metacentre  above  base. 

Centre  of  gravity  below  L.W.L. 
Centre  of  gravity  above  L.W.L. 

Prismatic  coefficient. 

Indicated  horse  power. 

Effective  horse  power. 

Nominal  horse  power. 

Length  of  ship  between  perpendiculars. 

Length  of  ship  on  load  water  line. 

Water  line. 

Length  of  ship  over  all. 

Placed  before  dimensions  indicates  that  these  are  the 

registered  or  tonnage  dimensions. 
Moment  of  inertia  of  load  water  plane. 
Metacentre  and  moment. 
Moment  to  alter  trim  one  inch  at  load  line. 

On  drawings  locates  the  intersection  of  projected  water 

line  with  the  elevation. 
Centre  of  gravity,  or  moment  about  centre. 

Centre  of  gravity  of  water  line. 

Centre  of  gravity  of  mid-section  area. 

Centre  of  gravity  of  sail  plan,  or  centre  of  effort. 

Ordinates  or  stations. 

Common  interval  or  abscissa  between  ordinates. 

Area  of  wetted  surface. 

Resistance. 

Half-girth  of  midship  section  (Lloyd's). 

Draught  of  water  moulded  (mean). 

Draught  of  water  forward  ^ 

Draught  of  water  aft  >  to  bottom  of  keel. 

Mean  draught  ) 

Power. 

Speed  in  knots  per  hour. 

,    .    ,  D§  x  T™ 

Admiralty  constant  = 


I.H.P. 


Per. 


Vlll 


Symbols   Common  in   Naval  Architecture 


rr 


Per  inch  ;  also  tons  per  inch  of  immersion  at  L.  W.  L. 

Square  foot. 
Square  inch. 


D".    .   . 

f Cubic  foot. 


Algebraical  Signs. 


Positive. 


Nega- 


Isto 


-|-  Plus,     addition. 
Compression. 
—  Minus,    subtraction. 

tive.     Tension. 
=  Equal  to. 

Unequal  to. 

Greater  than. 

Not  greater  than. 

Less  than. 

Not  less. 

By.     Multiplied  by 

Multiplied  by.    Ratio 

So  is.  As  (ratio).   Divided  by 

Perpendicular  to. 

II    Parallel  to. 

-rr  Not  parallel. 

V  Because. 

.'.  Therefore. 

/_  Angle. 

L  Right  angle. 

A  Triangle. 

O  Parallelogram. 

□   Square. 

O  Circumference. 

O  Circle. 


> 

< 

< 

X 


_L 


££S  Semicircle. 
Q  Quadrant. 

co  Infinity. 

O  Arc. 

<-»~  Difference. 

0   [  ]    [ !   Vincula. 
c   Constant. 
d  Differential. 
/  Integration. 
/  Functions. 
.g   Gravity. 
k   Coefficient. 
n   Any  number. 
a    An  angle. 
8    Variation. 
A  Finite  difference. 
0,  <f>  Any  angles. 

7T   Ratio  of  circumference  to  di- 
ameter of  circle. 
p    Radius. 
2  Sum  of  finite  quantities. 

V  Square  root. 

V  Cube  root. 

V  wth  root. 


IX 


THE 

NAVAL  CONSTRUCTOR 


CHAPTER   I. 

DISPLACEMENT    (D). 

The  displacement  of  any  floating  body  whether  it  be  a  ship,  a 
barrel,  a  log  of  lumber  or,  as  in  the  case  of  the  great  Philosopher 
who  first  discovered  its  law,  the  human  person,  is  simply  the 
amount  of  water  forced  or  squeezed  aside  by  the  body  immersed. 
.The  Archimedian  law  on  which  it  is  based  may  be  stated  as  :  — 
All  bodies  on  being  immersed  in  a  liquid  push  aside  a  volume  of  the 
liquid  equal  in  weight  to  the  weight  of  the  body  immersed.  From 
which  it  will  be  evident  that  the  depth  to  which  the  body  will  be 
immersed  in  the  fluid  will  depend  entirely  on  the  density  of  the 
same,  as  for  example  in  mere  my  the  immersion  would  be  very 
little  indeed  compared  with  salt  water,  and  slightly  less  in  salt 
water  than  in  fresh.  It  is  from  this  principle  that  we  are  enabled 
to  arrive  at  the  exact  weight  of  a  ship,  because  it  is  obvious  that 
if  we  can  determine  the  number  of  cubic  feet,  or  volume  as  it  is 
called,  in  the  immersed  body  of  a  ship,  then,  knowing  as  we  do 
that  there  are  35  cubic  feet  of  salt  water  in  one  ton,  this  volume 
divided  by  35  will  equal  the  iveight  or  displacement  in  tons  of  the 
vessel.  If  the  vessel  were  of  box  form,  this  would  be  a  simple 
enough  matter,  being  merely  the  length  by  breadth  by  draught 
divided  by  35,  but  as  the  immersed  body  is  of  curvilinear  form, 
the  problem  resolves  itself  into  one  requiring  the  application  of 
one  of  a  number  of  ingenious  methods  of  calculation,  the  principal 
ones  in  use  being  (1)  The  Trapezoidal  Rule,  (2)  Simpson's  Rules, 
and  (3)  Tchibyscheffs  method. 

Simpson's  First  Rule. 

The  calculation  of  a  curvilinear  area  by  this  rule  is  usually 
defined  as  dividing  the  base  into  a  suitable  even  number  of  equal 
parts,  erecting  perpendicular  ordinates  from  the  base  to  the  curve, 
and  after  measuring  off  the  lengths  of  these  ordinates,  to  the  sum 

1 


2  The  Naval  Constructor 

of  the  end  ones,  add  four  times  the  odd  and  twice  the  even  ordi- 
nates.  The  total  sum  multiplied  by  one  third  the  common  inter- 
val between  these  ordinates,  will  produce  the  area.  It  should, 
however,  be  stated  that  the  number  of  equal  parts  need  not  neces- 
sarily be  even,  and  as  it  is  sometimes  desirable  to  calculate  the 
area  to  an  odd  ordinate  by  taking  the  sum  of  the  first  ordinate 
and  adding  to  it  four  times  the  odd  ones,  and  twice  the  last  as  well 
as  the  even  ordinates  into  one  third  the  common  interval,  the  area 
may  be  calculated  accurately.  In  the  foregoing  definition  it 
should  be  noted  that  the  first  ordinate  is  numbered  "0,"  and  that 
the  number  of  intervals  multiplied  by  3  should  equal  the  sum  of 
the  multipliers. 


V* 


Vz 


V, 


nc > 


-a? — > 


-oe~ > 


B 


Fig,  1. 


x 


Area  of  ABCD  =  ^  (y0  +  4 yx  +  2 y2  +  4  2/3  +  y±). 

And  if  half  ordinates  be  inserted  between  y0  and  yx  and  between 
2/3  and  2/4  we  should  then  have  :  — 

x 
Area  =  ^  (i  y0+  2  y^+  \\  yx+±  y2+  1\  2/3+  2  y^  +  \  ?/4). 

Should,  however,  we  desire  to  calculate  the  area  embraced  within 
the  limits  of  y%  only,  omitting  the  half  ordinate  y^  then  :  — 

x 
Area  =  -  (y0  +  4  yx  +  2  y2  +  2  ?/3). 

So  that  it  is  immaterial  what  subdivision  of  parts  we  may  use  as 
long  as  the  multiplier  is  given  the  relative  value  to  the  space  it 
represents  as  exemplified  in  the  subjoined  table.  It  will  be  obvi- 
ous that  we  may  also  give  multiplier  only  half  its  value,  as 


i  y0  +  2  ?/i  +  1  y2  +  2  y6  +  \  y±, 


Multipliers  for  Subdivided   Intervals 


and  multiply  the  sum  by  §  ofx,  which  will  be  found  the  more  con- 
venient way  to  use  the  rule,  involving  as  it  does  iiguring  with 
smaller  values. 

Multipliers    for    Subdivided    Intervals. 


Ordinate. 

0 

* 

1 

2 

Q 

4    ■"»      5 : 

Multipliers, 

1 

•1 

1* 

4 

2 

4 

H 

1 

Ordinate-. 

0 

1 

2 

n 

3 

3i 

3 

3^ 

4 

A* 

[ 

4$ 

42 

* 

I 

5 

Multipliers, 

1 

4 

H 

2 

3 

T 

1 

1 

A 

2. 
3 

i 

1 

f 

1 

IT 

Ordinates, 

0 

i 
ft 

1 

H 

2 

2i 

3     4 

0 

6* 

6 

6I 

8* 

8| 

i 

Multipliers, 

i 

2 

1 

2 

1 

2 

H 

4 

M 

J 

3 

1 

4 

1 

1 
T 

Ordinates, 

0 

1 

2 

2* 

-- 

3 

H 

3f 

4 

5 

6 

6^ 

7 

71 

8 

Multiplier-. 

1 

4 

H 

H 

2 
3 

H 

2 
3 

H 

H 

4 

H 

2 

1 

2 

1 

1 

As  proof  of  the  rule  let  us  deal  with  an  example  : 

Area  ABCD  =  |  (y0  +  4  yx  +  |fc). 

Assume   curve   DFC    is   part   of    a  common   parabola ;    area 
DKCFD  is  f  area  of  parallelogram.     Join  DC,  and  draw  parallel 

H 


Fig.  2. 


to  GH  touching  curve.     If  DFC  be  part  of  parabola  area,  DFC 
is  §  of  parallelogram  DCHG. 

EK=\  {yo  +  yi).  FK=Vl-1 


2 


Parallelograms  on  same  base  and  between  same  parallels  are  equal. 
Draw  through  G  and  II  two  lines  parallel  to  base  as  GM  and  DL, 
then  area 

DCHG  =  area  DLMG 
=  2  x  x  J)G 
=  2  xx  FA' 

2/0  + 2/-/ 


-»■(*-*£») 


The  Naval  Constructor 


Area  BFC  =  |  of  above  =  *£(Vl-  ^IjM1 


Area  ABCKD  =  2  x  ( V-~  +  ^  J 

wu  1  o      /2/o  ,  2/2  \      4  x  /  2/0  +  2/2  V 

Whole  area  2  a;  ( -^  +  -^  )+  ^l^-  — 2 —  j 

=  5  (Z/o  +  4  ?/i  +  //j). 

Simpson's  second  rule  for  determining  areas  bounded  by  a  par- 
abola of  the  third  order  and  the  "five  eight"  rule  applicable  to 
the  calculation  of  one  of  the  subdivided  areas  are  given  in  most 
text-books,  but  are  omitted  here  as  superfluous,  Simpson's  first 
rule  being  adaptable  to  either  of  these  cases,  so  that  for  all  ship 
calculations  where  areas,  volumes,  or  moments  are  required,  the 
first  rule,  or  as  hereafter  explained  Tchibyscheff's  rule,  are  recom- 
mended. 

We  have  seen,  then,  how  the  area  or  surface  may  be  calculated 
by  this  rule,  and  as  the  volume  is  the  area  by  the  thickness,  it  will 
be  evident  that  if  the  areas  be  calculated  at  various  levels  or 
water  lines,  as  shown  in  the  figure,  and  these  areas  in  turn  treated 
as  a  curve  and  integrated  by  means  of  the  rule,  that  the  result  will 
be  the  volume  of  the  body. 


L.W.L. 

4  W.L. 

Ill          \    ^ 

W  /     III 

3  W.L. 

2  W.L. 

1  W.L. 
BASE 

\\\    \             \      \ 

/  9 

8/       / 

1 

\$C 

\2 

/   /  7/e// 

5N^^^^ 

//   /0^^"5 

Fig.  3. 

Let  the  Figs.  3  and  4  represent  the  immersed  half  longitudinal 
body  of  a  vessel  100  feet  long  by  12  feet  broad  submerged  to  5 
feet  draught  as  represented  by  L.W.L.  It  is  required  to  calculate 
the  volume  of  water  displaced  by  Simpson's  first  rule.  The  base 
line  length  between  perpendiculars  should  be  divided  into  an 
equal  number  of  intervals,  and  as  advocated  in  the  chapter  on 
Design,  it  will  be  well  to  have  a  definite  number  and  retain  same 
for  all  designs,  as  by  so  doing  it  will  facilitate  comparisons  and 
working  from  one  design  to  another.  Ten  such  intervals  with 
half-end  ordinates  is  a  very  convenient  division,   and  in  this  case 


Displacement  Sections 


will  give  a  common  interval  of  10  feet.  The  draught  of  5  feet 
must  likewise  be  subdivided  into  a  certain  number  of  equal  inter- 
vals, which  in  this  case  we  will  fix  at  4,  so  that 

5  ft.  draught 


=  1.25  ft. 


interval  between  water  lines.  These  divisions  of  water  lines  must  be 
drawn  across  the  body  plan  of  ten  sections,  and  the  half  breadths 
read  off  with  a  scale  and  tabulated  as  in  table  on  following  page. 


ai5>#y  T ^\  ^'^^fir^ 


s 


I    L 


[yyate'ALine 


las* 


ti'fU 


A^ 


T: 


L.W.L. 


FlG.  4. 

It  should  be  stated  in  connection  with  the  subdivision  of  the 
base  line  that  the  length  taken  for  displacement  is  measured  by 
some  designers  from  the  after  side  of  body  post  i.e.,  ignoring  the 
propeller  aperture  ;  and  by  others  from  the  fore  side  of  body  post 
to  the  after  side  of  stem  omitting  the  moulded  size  of  these  for- 
giugs.  Both  of  these  methods  are  inaccurate  besides  leading  to 
confusion,  as,  in  the  first  case,  the  displacement  of  the  propeller 
with  its  boss  will  equal  the  displacement  cut  out  for  aperture  not 
to  mention  the  volume  of  the  rudder,  which  is  rarely,  if  ever, 
taken  into  account.  And  in  the  second  case  the  tiny  amount  of 
displacement  added  at  the  knuckle  formed  by  the  bearding  line  of 
plating  when  the  length  is  taken  to  forward  and  after  sides  of 
stem  and  stern  post  respectively,  is  compensated  for  by  the  gud- 
geons on  stern  post.  Therefore  the  most  correct  and  also  the 
most  convenient  length  is  from  after  side  of  rudder  post  to  for- 
ward side  of  stem  at  load  water  line. 

Where  vessels  have  a  very  flat  iioor  line  a  half  water  line  should 
be   taken    be- 
tween base  line 

t 


and  first  water 
plane,  and  the 
keel  or  bottom 
half-breadth 
given  a  value 
proportioned  to 
the  rise  of  floor 
line  as  in  Fig.  5. 


Ke, 


Fi<;. 


G 


The   Naval   Constructor 


Required  the  half-breadth  x  at  the  keel  for  the  displacement 
sheet,  where  10  feet  is  the  actual  scaled  length  L,  6"  the  rise  of 
floor,  7"  the  distance  from  the  rise  line  to  first  water  line  at 
moulded  half-breadth  of  ship  and,  of  course,  13  inches  the  water 
line  interval,  then  :  — 

13" :  7"::  10  feet  :  x. 

.-.  x  =  5.38  feet  =  bottom  breadth. 


Displacement  Table. 


Water  lines  apart 
Ordinates  apart    . 


1.25/ 
10.00' 


Load  draught  ....    5.0(y 
Displacement  length,  100.00' 


02 
W 

H 
< 
ft 

3 
o 

Simpson's 
Multipliers. 

Keel. 

W.L.  1. 

W.L.  2. 

W.L.  3. 

W.L.  4. 

EG 

A 
+9 

.04 

en 

49 

S 
tj 
0 
u 

Ph 

.01 

OB 

0B 

P 

o 

Ph 

0B 

■a 

0:25 

W 
.04 

DO 

49 
U 

3 

O 
u 

Ph 

00' 

A 

49 

-d 
.04 

00 

49 

O 
u 

A 
49 

■A 

eecq 
W 

.04 

CO 

49 

O 
P 

0 

h 

Ph 

0 

.04 

.01 

.01 

.01 

.01 

1 

1 

.03 

.03 

.08 

.08 

.18 

.18 

.43 

.43 

1.41 

1.41 

1 

3 

4 

.02 

.01 

.16 

.12 

.73 

.55 

1.78 

1.33 

3.10 

2.32 

2 

2 

.02 

.04 

.92 

1.84 

2.35 

4.70 

3.78 

7.56 

4.81 

9.62 

3 

1 

.02 

02 

2.13 

2.13 

4.03 

4.03 

5.16 

5.16 

5.56 

5.56 

4 

2 

.02 

.04 

3.20 

6.40 

4.98 

9.96 

5.67 

11.34 

5.96 

11.92 

5 

1 

.02 

.02 

3.54 

3.54 

5.20 

5.20 

5.80 

5.80 

6.00 

6.00 

6 

2 

.02 

.04 

3.00 

6.00 

4.66 

9.32 

5.34 

10.68 

5.58 

11.16 

7 

1 

.02 

.02 

2.00 

2.00 

3.58 

3.58 

4.42 

4.42 

4.87 

4.87 

8 

2 

.02 

.04 

1.25 

2.50 

2.28 

4.56 

3.04 

6.08 

3.57 

7.14 

9 

3 

.02 

.01 

.48 

.36 

1.00 

.75 

1.50 

1.12 

1.90 

1.42 

9| 

1 

.02 

.02 

.18 

.18 

.50 

.50 

.74 

.74 

.97 

.97 

10 

1 

? 

15 

Sum 
of 

Mul- 
tipli- 
ers. 

03 

.01 

.03 

.01 

15 
=  10 

xl.5 

Sum 

of    .30 
Prod- 
ucts. 

i 

25.16 
■                2( 

43.34 

54.68 
\)              2(1 

62.41 
)                \ 

.15     +     50.32     +     43.34    +  109.36    +     31.20 

=  234.37 

(f  W.L.  interval)  X  (|  ordinate  interval)  x  2  (both  sides) 


35  (cub.  ft.  of  S.  W.  in  a  ton) 
_(1.25x|)x(10xf)x2 


coeff. 


35 


=  .315. 


Area  of  Water   Plane 


234.37 
x  .315 

Displacement  to  W.L.  4 =    73.82 

.15      +      50.32      +      43.34      +      54.68      =148.49 

x  .315 

Displacement  to  W.L.  3 =   46.77    tons. 

.15      +      50.32      +      21.6|  =    72.09 

x  .315 
Displacement  to  W.L.  2 =   22.70    tons. 

.15      +      25.16  =    25.31 

x  .315 
Displacement  to  "W.L.  1 =     7.97    tons. 

The  displacement  to  the  load  water  line  being  73.82  tons  it  is 
useful  to  know  what  relation  that  weight  bears  to  the  vessel  if  she 
were  of  box  section,  in  other  words,  the  amount  that  has  been  cut  off 
the  rectangular  block  formed  by  the  length,  breadth,  and  draught, 
to  fine  it  to  the  required  form,  or  the  block  coefficient  or  coeffi- 
cient of  displacement  represented  by  the  symbol  "J",  It  will 
be  evident  that  this  coefficient  may  readily  be  computed  by  mul- 
tiplying the  length  x  breadth  X  draught,  and  dividing  the  product, 
which  is  the  volume  of  the  box  in  cubic  feet,  by  35  to  get  the  tons 
displaced  by  the  rectangular  block.  The  displacement  as  calcu- 
lated, divided  by  this  result,  will  give  the  block  coefficient  "  5  ",  or, 

V 

=r z=.432  nearlv. 

L  x  Bxd 

The  range  of  this  coefficient  for  various  types  is  given  else- 
where in  the  Table  of  Element  Coefficients. 

Area  of  Water  Plane. 


Keel. 

W.L.  1. 

W.L.  2. 

W.L.  3. 

W.L.  4. 

Sum  of  products 

-  'Ommon  interval, 

Half-areas  . 

Areas    of    water 

planes 

.30 

25.16 
6f 

43.34 

288.93 
2 

54.68 
6f 

62.41 
6f 

2.00 
2 

167.73 
2 

335.46 

364.63 
2 

416.07 
2 

4  00 

.",77.  v'"> 

729.06 

832.14 

The  area  of  any  of  the  water  planes  in  the  specimen  displace- 
ment table  will  simply  be  the  sum  of  the  products  of  the  particular 


8 


The   Naval   Constructor 


water  plane  required,  multiplied  by  §  the  interval  between 
ordinates.  This  product  doubled  will  be  the  total  area  of  both 
sides. 

Tons  per  Inch  of  Immersion  OP")* 

It  is  useful  to  know  the  amount  of  displacement  of  the  vessel 
for  each  inch  of  immersion  at  various  draughts,  as  from  this 
data  small  amounts  of  cargo  taken  out  or  placed  on  board  can  be 
accurately  determined  without  reference  to,  or  scaling  from,  the 
regular  displacement  curve.  It  will  be  seen  that  if  A  represents 
the  area  of  water  plane,  that  this  surface  multiplied  by  a  layer 
1  inch  in  thickness  and  divided  by  12  will  equal  the  volume  of 
water  displaced  in  cubic  feet  at  the  particular  water  plane  dealt 
with,  and  that  this  volume  divided  by  35  will  equal  the  displace- 
ment in  tons  for  one  inch,  or  in  other  words,  the  tons  per  inch 
immersion.     Or, 

A  X  12  =  12  CUbic  fe6t' 
and  the  weight  of  water  in  the  layer 

i^ x  ^ = ^o  =  tons  per  inch- 

Tons  per  inch  immersion  in  salt  water, 

area  of  water  plane 
420 
Tons  per  inch  immersion  in  fresh  water, 

area  of  water  plane 
(12  x  36)  =  432 

So  that  referring  to  the  table  we  have  been  working  out,  we  get :  — 


Keel. 

W.L.  1. 

W.L.  2. 

W.L.  3. 

W.L.  4. 

Area  of  water  plane 

12"  X  35  =     .     .     . 

Tons  per  inch  = 

4.00 

420 
.01 

335.46 

420 

.79 

577.86 

• 

420 
1.37 

741.06 

• 

420 

1.76 

832.14 

420 
1.98S.W. 

It  is  often  necessary  to  estimate  the  tons  per  inch  approxi- 
mately, and  for  this  purpose  the  coefficient  of  the  load  line  or 
"a"  is  used.  The  method  of  arriving  at  this  coefficient  is  ex- 
plained in  the  chapter  on  design  when  the  displacement  is  known. 


Immersion,   from   Salt  to    Fresh   Water        9 

It  has  a  range  of  about  .<>  in  fine  vessels  to  .0  in  exceptionally 
full  ones.     In  the  above  example  it  is  found  to  be 

832.14  832.14       ofxl 


Length  x  Breadth       1200 
Therefore  the  tons  per  inch  is  equal  to 

L  X  B  X  -6t)4  -  !  OR 
420 

Its  relation  to  the  other  element  coefficients  is 

5 
a  —  —  • 
e./3 

Immersion  Passing  from  Salt  to  Fresh  Water. 

From  what  has  been  previously  said  it  will  be  obvious  that  the 
draught  of  water,  or  immersion  of  a  vessel,  will  undergo  a  change 
in  passing  from  fresh  water  into  the  sea  or  vica  versa,  owing  to 
the  difference  in  density  of  the  two  liquids.  If  we  take  the  case 
of  the  ship  passing  from  salt  water  to  fresh,  the  immersed  volume 
will  be  in  each  case  as  follows  :  — 

Immersed  volume  in  salt  water     =  35  Z), 
Immersed  volume  in  fresh  water  =  36  Z>, 

where  D  is  the  displacement  in  tons,  which  in  the  example  we 
have  been  investigating  equals  73.82  tons.  Therefore  the  volume 
in  cubic  feet  which  the  vessel  has  sunk  on  entering  the  fresh 
water  is  36  D  -  35  D  =  2657  -  2584  =  73  cubic  feet.  Let  T  =  tons 
per  inch  immersion  in  fresh  water  .  \  area  of  water  plane  =  432  T 
and  the  extent  to  which  the  vessel  will  sink 


73     .  12  X  73 


o 


_  feet  =  . — - —  =  — —  =  L02  inches. 

432  T  432  r  inches      M  f 

Inversely  we  have  the  amount  that  the  vessel  emerges  in 
passing  out  of  a  river  into  the  ocean.  Thickness  of  the  layer 
which  vessel  has  risen  in  feet 

_Difference  in  volume  D 

Area  of  the  plane 
and  in  inches, 

Difference  in  Volume  I)  x  12      12  X  73       73 


=  1.05  inches. 


Area  of  water  plane  420  T       69.3 

This  immersion  and  emersion  is,  of  course,  the  mean  amount  as 
the  vessel  will  also  slightly  change  her  trim  due  to  the  altered 
position  of  the  centre  of  gravity  of  water  plane,  about  which  the 
ship's  movements  are  pivotal. 


10 


The  Naval   Constructor 


Area  of  Midship  Section  (X  A). 

The  area  of  this,  or  any  of  the  other  sections  on  the  displace- 
ment table,  is  calculated  by  taking  the  half-breadths  of  the 
water  lines  and  integrating  them  as  explained  for  water-line  area. 
The  sum  of  the  products  thus  obtained  is  multiplied  by  §  the 
distance  of  water  lines  apart,  and  that  result  by  2  for  both  sides. 
Where  the  vessel  has  little  rise  of  floor  a  half  water  line  should  be 
introduced,  and  the  bottom  half-breadth  proportioned  to  the  rise 
line,  as  pointed  out  in  the  displacement  calculation.  In  the 
example  with  which  we  are  dealing,  however,  the  vessel  has 
considerable  rise,  so  that  this  subdivision  has  been  omitted. 


Ordinate. 

Keel. 

W.L.  1. 

W.L.  2. 

W.  L.  3. 

W.L.  4. 

"5" 

Half- 
Breadth. 

Half- 
Breadth. 

Half- 
Breadth. 

Half- 
Breadth. 

Half- 
Breadth. 

Simpson's 
Multipliers 

.02 

l 

2 

3.54 

2 

5.20 

1 

5.80 
2 

6.00 

l 
5 

.01     +     7.08    +    5.20    +  11.60    +   3.00 

=  26.89 

|  distance  between  water  lines x  .83 

Half  area  of  midship  section  to  L.  W.L.      .     .     .    =22.31 

For  both  sides x  2 

Midship  section  area =44.62 

The  coefficient  of  this  area,  or  /3,  is  a  very  important  element 
of  the  design  as  explained  elsewhere,  and  is  obtained  by  dividing 
the  midship  area  by  the  area  of  the  rectangle  formed  by  the 
molded  breadth  and  the  draught,  or 


Mid.  area 


Breadth  X  draught 


44.62 


=  .743  coefficient  of  mid.  area. 


Its  relation  to  the  midship-section  cylinder  or  prismatic  co- 
efficient  "_p"  is  —  1  and  "pM  is  equal  to  the  volume  of  dis- 
placement divided  by  the  length  x  mid.  area,  thus  :  — 

V          LxBxdxdS  _ 

p  — = =  —  =  prismatic  coefficient, 

LX.A      L  x  B  x  dx  p     p 

5 


and  consequently, 


0  = 


P 


Centre  of  Buovancv  1  1 

Centre  of  Buoyancy  (C.B.). 

The  centre  of  buoyancy  of  the  displaced  water  is  simply  its 
centre  of  gravity,  and  its  location  below  the  load-water  line  is 
greater  or  less  in  accordance  with  the  form  of  the  immersed  body. 
This  distance  may  be  found  by  dividing  the  under-water  part  into 
a  number  of  planes  parallel  to  the  load  line,  and  multiplying  the 
volumes,  lying  between  these  water  planes,  by  their  depth  below 
load-water  line.  These  moments  divided  by  the  displacement 
volume  will  give  the  location  of  centre  of  buoyancy  below  load- 
water  plane.  So  that  by  taking  the  functions  of  the  products  at 
each  water  plane  on  the  sheet  we  have  been  working  and  multi- 
plying them  by  the  number  of  the  water  line  they  represent 
below  L.W.L.,  and  dividing  the  sum  of  those  products  by  the 
sum  of  the  functions  referred  to,  we  shall  have  the  number  of 
water-line  intervals  (or  fraction  of  an  interval),  which  the  C.B. 
is  below  load-water  line.  This  result,  multiplied  by  the  common 
interval  between  water  lines,  will  give  the  required  distance  in 
feet. 

Keet,.     W.L.  1.      W.L.  2.        W.L.  3.       W.L.  4. 

1  products^    |   15  +  5032  +  4334  +  m36  +  3L2°  =  23437 
4  3  2 1  0  ' 

.60  +150.96  +  86.68  +  100.36  +      ~7>  =  347.60 

347.6 -i- 234.37  =      1.49 

x 
Water  lines  apart =       i  .25 

Centre  of  buoyancy  below  W.L.  4 =       1.86ft. 

The  centre  of  buoyancy  may  be  determined  from  the  displace- 
ment curve  by  calculating  the  area  enclosed  within  the  figure 
formed  by  the  vertical  line  representing  the  draught  of  5  ft., 
the  horizontal  line  equal  to  the  tons  displacement  at  this  draught 
and  the  curve  itself.  This  area  divided  by  the  length  of  the  hori- 
zontal line  referred  to,  will  give  the  depth  of  C.B.  below  L.W.L. 
In  the  present  example  we  have  :  area  =  13*. 6"  sq.  feet,  and 
length  of  horizontal  line  (displacement  in  tons)  =  73.82,  and 

^=1'87feet' 

distance  of  C.B.  below  L.W.L. 

A  like  result  may  also  be  obtained  by  taking  the  sum  of  the 
products  of  each  water  line,  and  dividing  them  by  the  sum  of 
Simpson's  multipliers.  The  mean  half-breadths  of  water  lines 
so   obtained    may  be   then  used  to   draw  a  mean  section  of  the 


12 


The   Naval   Constructor 


vessel  on  stout  paper,  which  on  being  cut  out  with  a  knife  and 
swung  in  two  positions,  the  points  being  intersected  afterwards, 
will  give  the  centre  of  gravity  (buoyancy)  very  accurately. 

Various   approximate    methods   are   in  vogue   for  finding   this 
centre,  some  of  which  are  fairly  accurate. 

— a ) ' 

(2)   Approx.  C.B.  below  L.W.L.  =-(- +  —  ), 

where  A  is  the  area  of  load-water  plane. 

This  centre,  as  will  be  explained,  has  an  important  bearing  on 
the  stability  of  the  ship. 

Centre  of  Buoyancy  Longitudinally  (L.C.B.). 


Ordin- 

ATES. 

Areas. 

Multi- 
pliers. 

Func- 
tions. 

Inter- 
vals. 

Moments. 

After 
Moment. 

0 

.24 

i 
% 

.06 

5 

.30 

1 

1.91 

1 

1.91 

41 

8.59 

1 

6.17 

3 

4.63 

4 

18.52 

2 

14.18 

2 

28.36 

3 

85.08 

3 

21.40 

1 

21.40 

2 

42.80 

4 

5 
6 

7 

25.71 

26.89 
24.14 
18.86 

2 

1 
2 
1 

51.42 

26.89 

48.28 
18.86 

1 

0 
1 

2 

51.42 

206.71 

48.28 

37.72 

Forward 
Moment. 

8 

12.65 

2 

25.30 

3 

75.90 

9 

5.92 

3 

4.44 

4 

17.76 

n 

2.83 

1 

2.83 

44 

2 

12.74 

10 

.08 

1 
T 

.02 

5 

.10 

192.50 

Preponder- 
ating 
moment 

abaft.  Ordi- 
nate 5. 

1 

Functic 

n  of  disj 

)lacemenl 

j       •          •    

234.40 

1=14.21 

J 

.06  Interval  C.B.  abaft  5. 


14.21 
Common  Interval  =  10  ft.  x  .06  =  0.6  ft.  C.B.  abaft  No.  5. 


The  locus  of  the  centre  of  buoyancy  in  a  fore-and-aft  direction 
is  of  course  the  centre  of  gravity  of  the  displacement,  and  is  the 


Transverse    Metacentre  13 


pivotal  point  or  fulcrum  for  the  moments  of  all  weights  placed 
forward  or  aft  of  this  position.  It  will  be  obvious,  therefore,  that 
its  location  is  of  great  value  in  determining  the  trim  of  the  vessel, 
and  the  various  alterations  thereof  due  to  rearrangements  of 
weights  on  board.  Its  position  is  calculated  by  taking  the  areas  of 
the  sections  and  putting  them  through  the  multipliers  ;  these 
functions  of  areas  are  in  turn  multiplied  by  the  number  of  inter- 
vals, (each  one  is  forward  or  aft  of  the  mid-ordinate.)  and  the 
difference  between  these  forward  and  after  moments  divided  by 
the  sum  of  the  area  functions.  The  quotient  resulting  is  the 
number  (or  fraction)  of  intervals  that  the  centre  of  buoyancy  is 
forward  or  aft  of  the  \  length  according  as  the  moment  prepon- 
derates forward  or  aft  respectively. 

This  centre  should  be  calculated  for  various  draughts,  as  of 
course  it  changes  with  different  draughts  and  alterations  of  trim, 
owing  to  the  changing  relationship  between  the  fineness  of  fore 
and  after  bodies  at  different  immersions  and  trims. 

Transverse  Metacentre  (M.C.) 

The  position  of  this  element  is,  in  conjunction  with  the  centre 
of  gravity,  the  most  vital  in  the  design  of  the  ship.  As  its  name 
implies,  it  is  the  centre  or  point  beyond  which  the  centre  of  gravity 
of  the  ship  may  not  be  raised  without  producing  unstable  equilib- 
rium in  the  upright  position,  or,  otherwise  stated,  if  the  ship  be 
inclined  transversely  to  a  small  angle  of  heel,  the  centre  of 
buoyancy  which  originally  was  on  the  centre  line  will  move  out- 
board to  a  new  position  ;  but,  as  it  acts  vertically  upward,  it  must 
somewhere  intersect  the  centre  line.  This  point  of  intersection  is 
known  as  the  metacentre.  One  of  the  factors  in  the  determination 
of  its  location  above  the  centre  of  buoyancy  has  already  been 
calculated,  viz:  the  volume  of  displacement  V ;  the  other,  the 
moment  of  inertia  of  the  water  plane  about  the  centre  line  of  ship, 
we  shall  proceed  to  compute.  The  height  M  above  the  C.B.  or 
B.M.  is  found  by  :  — 

Moment  of  Inertia  of  Water  Plane  I       „  „ 

Or     nnl'.Jl. 

Volume  of  Displacement:  V 

The  moment  of  inertia  of  the  water  plane  is  a  geometrical 
measure  of  the  resistance  of  that  plane  to  "upsetting,"  or  when 
taken  about  the  centre  line,  as  in  the  case  of  calculating  for  trans- 
verse metacentre,  to  "careening.'1  So  that  the  greater  the  water- 
line  breadth  the  higher  will  be  its  value;  for  we  must  imagine  the 
water  plane  as  being  divided  into  a  great  number  of  small  are 
and  each  of  these  multiplied  by  the  square  of  its  distance  from  the 


14 


The   Naval   Constructor 


centre  line  of  ship,  when  the  sum  of  these  products  will  equal  the 
moment  of  inertia  of  half  the  water  plane,  about  the  middle  line 
of  vessel  as  an  axis.  As  both  sides  of  the  water  plane  are  sym- 
metrical, the  total  7  will  be  this  result  multiplied  by  2.  Applying 
this  principle  to  W.L.  4  in  the  example  with  which  we  are  con- 
cerned, we  get  the  following  tabular  arrangement :  — 

Moment  of  Inertia  of  Water  Plane  (7). 


Ordi- 

NATES. 

Half- 

Cubes  of 

Simpson's 

Breadths 

Half- 

Mul- 

Products. 

OF  W.L.  4. 

Breadths. 

tipliers. 

0 

..04 

•            •            • 

i 

4 

1 

2 

1.41 

2.74 

1 

2.74 

1 

3.10 

29.79 

3 
4 

22.34 

2 

4.81 

111.28 

2 

222.56 

3 

5.56 

171.88 

1 

171.88 

4 

5.96 

211.71 

2 

423.42 

5 

6.00 

216.00 

1 

216.00 

6 

5.58 

173.74 

2 

347.48 

7 

4.87 

115.50 

1 

115.50 

8 

3.57 

45.50 

2 

91.00 

9 

1.90 

6.86 

3 
4" 

5.14 

H 

.97 

•          •          • 

1 

•          •          • 

10 

.03 

•          •          • 

1 

■          •          • 

1,618.06 

f  CI.   .   • 6\6 

10,787.07 

2 
5 

Moment  of  Inertia =  7,191.38 

Volume  of  Displacement,  V =  2,583.70 

„  „         7       7191.38      n„„£ 

The  calculation  for  Moment  of  Inertia  and  Transverse  Meta- 
centre  above  C.B.  may  be  more  easily  remembered  if  we  treat  the 
cubes  of  water  line  half-breadths  as  the  ordinates  of  a  curve  two- 
thirds  the  area  of  which  will  equal  7,  and  this,  in  turn,  divided  by 
V  will  give  B.M. 

However,  when  we  know  a,  or  the  coefficient  of  water  line,  we 
may  arrive  very  accurately  at  the  moment  of  inertia  of  the  water 


Longitudinal    Metacentre  1  5 

plane,  and  consequently  at  the  B.M.  without  the  labor  of  the 
foregoing  calculation  by  multiplying  the  Length  by  the  Breadth3  by 
a  coefficient,  which  coefficient  will  be  determined  by  a  and 
selected  from  the  table  given  on  page  4s.  By  referring  to  this 
table,  we  find  for  a  (value  .<">04)  that  the  coefficient  '*»"  (inertia 
coefficient)  is  equal  to  .0414.  whence  we  get  1  —  L  x  W>  x  i  =  litO 
X  1l,;jx  .0414  =  71~>4  moment  of  inertia,  which  is  sufficiently  close 
for  all  purposes,  and  :  — 

B.M.  =  ^=  =  2.76. 

By  transposing  and  taking  the  calculated  7,  we  find 

7191 


100  x  12* 


= .0416. 


Longitudinal  Metacentre  (L.M.C.) 

From  the  definition  given  for  the  transverse  metacentre  it  will 
be  seen  that  if  the  ship  be  inclined  longitudinally,  instead  of,  as  in 
the  former  case,  transversely,  through  a  small  angle  that  the  point 
in  which  the  vertical  through  the  altered  C.B.  intersects  the 
original  one  will  also  give  a  metacentre  known  as  the  longitudinal, 
or  L.M.C.  Its  principal  use  and  value  are  in  the  determination  of 
the  moment  to  alter  trim  and  the  pitching  qualities  of  the  vessel, 
or  longitudinal  stabilitv.  It  will  be  obvious  that  the  moment  of 
inertia  of  the  water  plane  must  be  taken  through  an  axis  at  right 
angles  to  the  previous  case,  viz.,  at  right  angles  to  the  centre  line 
through  the  centre  of  gravity  of  water  plane,  which  will  be  where 
the  original  and  new  water  planes  cross  one  another  in  a  longitu- 
dinal view. 

h  of  Water  Plane  about  its  C.G. 


L.M.C.  above  C.B.  = 


Volume  of  Displacement 


Therefore,  to  calculate  the  M  I\,  we  must  figure  the  moment  of 
inertia  with,  say,  ordinate  5  (or  any  other  one)  as  an  axis  when 
the  moment  about  a  parallel  axis  through  the  centre  of  gravity 
plus  the  product  of  the  area  of  water  plane  multiplied  by  the 
square  of  the  distance  between  the  two  axes  will  equal  the  moment 
about  ordinate  5. 

The  moment  of  inertia  about  the  midship  ordinate  we  shall  call 
7,  and  the  distance  of  the  centre  of  gravity  from  this  station  =./•. 
The  moment  of  inertia  about  the  centre  of  gravity  of  plane  =  I\. 
We  then  have  1= I\+  Ax'2,  or  Ii  =  I  —  Ax2.  A  clearer  conception 
of  this  will  be  obtained  from  the  tabulated  arrangement. 


16 


The   Naval   Constructor 


Longitudinal  Metacentre. 

(Common  Interval  10  Feet.) 


a  . 

fa  H  ^ 

1           OB 
2     •    « 

Pro- 

EC 

Pro- 

. O 

M    fa        . 

Products 

Ordi- 

NATES. 

2  J  K 
CO   &  _ 

ducts 

for 

Area. 

fa 
> 
fa 
hi 

ducts 
for  Mo- 
ments. 

£faS 

for 
Moments 

of 
Inertia. 

0 

.04 

1 
4" 

.01 

5 

.05 

5 

.25 

1 

o 

1.41 

1 

1.41 

4i 

6.34 

4| 

28.53 

1 

3.10 

3 

2.32 

4 

9.28 

4 

37.12 

2 

4.81 

2 

9.62 

3 

28.86 

q 

86.58 

o 

5.56 

1 

5.56 

2 

11.12 

2 

22.24 

4 

5 

6 

596 
6.00 

5.58 

2 
1 

2 

11.92 

6.00 

11.16 

1 
0 
1 

11.92 

1 
0 
1 

11.92 
11.16 

67.57 

11.16 

7 

4.87 

1 

4.87 

2 

9  74 

2 

19.48 

8 

3.57 

2 

7.14 

3 

21.42 

3 

64.26 

9 

1.90 

3 
4~ 

1.42 

4 

5.68 

4 

22.72 

9| 

.97 

1 

.97 

4J 

4.36 

4.L 

19.62 

10 

.03 

1 

4 

.01 

5 

.05 

5 

.25 

62.41 

•   •   • 

52.41 

.   .   . 

324.13 

Area  of  water  plane  =  62.41  x(|x  10)  x  2. 

=  832.14  square  feet. 

Distance  of  centre  of  flotation  abaft  ordinate  5 


_  (67.57  -52.41)  10  _ 


62.41 


=  2.42  feet. 


Moment  of  inertia  of  water  plane  about  ordinate  5 

=  324.13  x  (|x  10)  x  102x  2  =  432,172  =  /. 

Moment  of  inertia  of  water  plane  about  axis  through  its  centre 
of  flotation. 

=  432,172  -  (832.14  X  2.42*)  =  427,304  =  Iv 

Longitudinal  metacentre  above  C.B. 

I       427,304 

tF  =  ..goo  n  =  165  feet  =  Longitudinal  B. M. 


Moment  to   Change   Trim  17 

An  excellent  approximate  formula  for  the  longitudinal  B.M.  is 
given  by  J.  A.  Normand  in  the  1H82  transactions  of  the  l.N.A 
Taking  the  Bymbols  we  have  been  using  :  —  7 

.  A*  XI 
L .  n .  M .  —  .0 1  oO  -n ==  ■ 

b  x  r 

Applying  this  formula  to  the  vessel  with  which  we  are  dealing, 
we  find  : 

I.^M..,,::;^14;*,'^  104.12  feet. 
12  x  2.>88.7 

which  is  a  very  close  approximation  to  the  calculated  result  of 
165  feet. 

We  may  also  use  the  approximate  formula  which  we  applied  in 
the  case  of  the  transverse  B.M.  altered  to  suit  the  new  axis  with  a 
modified  coefficient,  as  :  — 

L.B.M.  =  L*x  Bx  iv 

Moment  to  Change  Trim  (3fi). 

As  the  centre  of  gravity  of  the  displacement  (or  centre  of  buoy- 
oncy),  either  in  the  vertical  or  the  longitudinal  direction  may  be 
an  entirely  different  locus  from  the  ship's  centre  of  gravity,  it  is 
obvious  that  unless  the  moment  of  the  weights  of  the  ship  and 
engines,  with  all  equipment  weights,  balances  about  the  centre  of 
buoyancy  we  shall  have  a  preponderating  moment  deflecting  the 
head  or  stern,  as  the  moment  is  forward  or  aft  of  the  C.B.,  re- 
spectively, until  the  vessel  shall  have  reached  a  trim  in  which  the 
pivotal  point  or  C.B.  is  in  the  same  vertical  line  as  the  completed 
ship's  centre  of  gravity.  To  determine  the  moment  necessary  to 
produce  a  change  of  trim  (Mi)  in  a  given  ship,  it  is  necessary  to  know 
the  vertical  position  of  the  centre  of  gravity  of  the  vessel  and  the 
height  of  the  longitudinal  metacentre  (L.M.C.).  The  former  may 
be  calculated  in  detail  or  preferably  proportioned  from  a  similar 
type  ship  whose  centre  of  gravity  has  been  found  by  experiment  ; 
although  great  accuracy  in  the  location  of  this  centre  in  calculat- 
ing the  moment  is  not  as  important  as  in  the  case  of  G.M.  for 
initial  stability,  as  small  variations  in  its  position  can  only  affect 
the  final  result  infinitesimally.  To  investigate  the  moment  affect- 
ing the  trim,  let  us  move  a  weight  P  already  on  board  of  the  100- 
foot  steamer  whose  calculations  are  beinsr  figured. 

D  —  Weight  <>f  ship  including  weight  P  =  73.82  tons. 
BJf=  165  feet  P=5Tons. 

GM  -  160  feet.  I  =  GO  feet  (distance  moved). 

L  -  100  feet  (length  of  vessel). 


18 


The   Naval   Constructor 


In  the  figure  we  have  the  centre  of  gravity  G  to  G\,  and  the 
centre  of  buoyancy  from  B  to  J5i,  due  to  the  shifting  of  the  weight 
P  forward  for  a  distance  represented  by  Z,  giving  a  moment 

Dx  GGi  =  P  x  7,     and     GGX  =  — —  • 


g|___^1 


g1— 1g, 


Li 


Fig.  6. 


The  new  water  line  is  at  W\L\  and  B^Gi  are  in  the  same  verti- 
cal and  at  right  angles  to  it,  and  the  point  of  intersection  of  the 
original  and  new  water  line  at  "0"  equal  to  the  centre  of  gravity 
(flotation)  of  water  plane,  therefore  the  triangles  GMGi,  WOWi, 
and  LOLi,  are  of  equal  angle,  so  that 

GGt      WWX      LLi      WWr  +  LLr 


GM  ~    WO  ~  LO 


WO  +  LO 


But  WWi  +  LLiis  the  change  of  trim,  and  W0-\-L0 is  the  length 
of  the  vessel  =  X,  then 

change  of  trim      WWi  +  LL\ 


but  we  have  seen  that 


WO+LO 


GM  x  change  of  trim 
GG\  =  — 


P  Xl 


Then 


P  xlx L  .    . 
Change  of  trim  =  -^-^     feet. 


Substituting  the  values,  we  get :  — 
P  x  IX  L       5  X  .50'  x  100' 


I)  x  GM 


78.82  x  160 


D  x  GM 


=  2. 116  feet  =  24 l  inches. 


Calling  this  change  of  trim  24  inches,  and  assuming  that  the  point 
of  intersection  "  0  "  is  at  the  centre  of  the  length,  we  should  have 


Moment  to   Alter  Trim   One   Inch         19 

the  stem  immersed  12  inches  and  the  stern  raised  12  inches  from 
the  original  water  line,  the  sum  of  these  figures  equalling  the 
total  change. 

Moment  to  Alter  Trim  One  Inch  (M"). 

From  the  foregoing  it  will  be  seen  that  the  total  change  of  trim 
being  known  for  a  given  moment,  inversely  we  may  get  the 
amount  necessary  to  alter  the  trim  for  one  inch  only,  this  being  a 
convenient  unit  with  which  to  calculate  changes  of  trim  when  a 
complexity  of  varying  conditions  are  being  dealt  with.  As  we 
have  seen  P  x  1  =  Mx  the  moment  to  change  trim,  and 


therefore, 


Change  of  trim  =  ^  Xy  Qy[   feet  ; 


TV  foot  or  one  inch  =  — — —  =  M 

l~  12  x  L 


Substituting  values  we  have  :  — 


*- 


73.82  x  160' 
M  =      12  x  100     =9'M  toot-tons- 

In  designing  preliminary  arrangements  of  vessels,  it  is  necessary 
that  we  should  know  fairly  accurately  the  moment  which  it  will 
take  to  alter  the  trim  one  inch  (M")  to  enable  us  to  arrange  the 
principal  weights  in  the  ship,  and  the  varying  effects  on  the  trim 
consequent  on  their  alteration  in  position  or  removal.  For  this 
purpose  a  close  approximation  to  this  moment  (Jf)  is  desirable 
and  may  be  calculated  from  Normand's  formula  as  follows  : 

Af"=  ~  .0001725. 

Where  J.2  =  the  square  of  the  water  plane  area,  and  i?  =  the  great- 
est breadth  of  water  plane.  Applying  this  approximate  formula 
to  the  foregoing  example,  we  have  :  — 

832  142 
W  -  -  x  .0001725  =  9.95  foot-tons, 

as  against  9.84  foot-tons  found  by  actual  calculations,  a  difference 
too  insignificant  to  affect  noticeably  the  change  in  trim. 

This  moment  is  useful  to  have  for  various  draughts,  and  con- 
sequently should  be  calculated  for  light  and  load  conditions,  and 
for  one  or  two  intermediate  spots  and  a  curve  of  M"  run  on  the 
usual  sheet  of  "  Curves  of  Elements.'' 


20 


The   Naval   Constructor 


Alteration   in   Trim   through   Shipping   a   Small 

Weight. 

If  it  be  required  to  place  a  weight  on  board  but  to  retain  the 
same  trim,  i.e.,  to  float  at  a  draught  parallel  to  the  original  one, 
the  weight  added  must  be  placed  vertically  above  the  centre  of 
gravity  of  the  water  plane.  Should,  however,  the  weight  be  re- 
quired in  a  definite  position,  then  the  altered  trim  will  be  as 
under  :  — 


Fig.  7. 


Instead  of  dealing  with  the  weight  at  P  let  us  assume  firstly 
that  it  is  placed  on  board  immediately  over  the  C.G.  of  water 
plane,  when  we  shall  find  the  parallel  immersion  to  be  a  layer 

P 
equal  to  the  distance  between  WL  and  W\LX  whose  depth  is 


Let  the  weight  be  now  moved  to  its  definite  position  at  a  distance 
I  forward  of  C.G.,  then 

ftr      •  PXlX      L 

Change  of  trim  =  -  +  p)  QM  =  C. 

GM  of  course  will  be  the  amended  height  due  to  altered  con- 
dition after  the  addition  of  P.     Then  :  — 

C        P 

Draught  forward  =  — -  -f 


a 


Draught  aft 


C_ 
2 


'/ 


Of  course  we  assume  that  the  alteration  is  of  like  amount  for- 
ward as  aft.  This  is  only  partly  correct,  but  where  small  weights 
are  dealt  with  is  sufficiently  so  for  most  purposes.  Generally  the 
ship  is  fuller  aft  on  and  near  the  load  line  than  forward,  and  prob- 
ably a  water  plane  midway  between  base  and  L.W.L.  would  have 
its  centre  of  flotation  at  the  half  length,  so  that  a  curve  drawn 
through  the  centres  of  gravity  of  the  water  planes  would  incline 
aft,  and  as  we  have  assumed  the  weight  as  being  placed  on  board 
over  the  C.G.  of  the  original  water  plane,  it  is  obvious  that  the 


Tchibyscheff's   Rule  21 

new  line  will  have  its  centre  of  flotation  somewhat  further  aft, 
and  consequently  the  tangent  of  the  angle  nyMl'..  will  be  l< 
than  that  of  LiOL-2-  With  large  weights  and  differences  in  the 
two  draughts,  the  disparity  would  become  sufficiently  great  to 
require  reckoning,  in  which  event  the  assumed  parallel  line  in  the 
preceding  case  would  give  the  water  line  from  which  to  determine 
the  centre  of  flotation.  Thereafter  on  finding  the  change  of  trim, 
which  we  shall  call  10  inches,  the  amount  of  immersion  of  stem 
and  emersion  of  stern  post  would  be  in  proportion  to  the  distance 
from  Oto  stem  and  Oto  post  relatively  to  the  length  of  water  line. 
If  we  call  "  0  '*  to  stem  CO  feet  and  "  0  "  to  post  40  feet,  the  water 
line  length  being  100  feet,  we  have  :  — 

Immersion  forward  y6^  x  10"  =  0  inches  }  Total  change 
Emersion  aft  ^^  x  10    =4  inches)      10  inches. 

TCHIBYSCHEFF'S    RULE. 

In  the  preceding  pages  we  have  treated  with  the  common  appli- 
cation of  Simpson's  first  rule  to  ship  calculations.  Another 
method,  equally,  if  not  more  simple,  which  is  slowly  gaining 
favor  with  naval  architects  is  that  devised  by  the  Russian  Tchi- 
byscheff .  This  rule  has  the  great  advantage  of  employing  fewer 
figures  in  its  application  ;  more  especially  is  this  the  case  in  deal- 
ing with  stability  calculations,  and  its  usefulness  in  this  respect 
is  seen  in  the  tabular  arrangement  given  here.  It  has  the  addi- 
tional advantage  of  employing  a  much  less  number  of  ordinates 
to  obtain  a  slightly  more  accurate  result  and  the  use  of  a  more 
simple  arithmetical  operation  in  its  working  out,  viz.  addition. 
As  the  ordinates,  however,  are  not  equidistant,  it  has  the  dis- 
advantage of  being  inconvenient  when  used  in  conjunction  with 
designing,  and  for  this  reason  its  use  is  advocated  for  the  finished 
displacement  sheet  and  calculations  for  G.Z. 

■  The  rule  is  based  on  a  similar  assumption  to  Simpson's,  but  the 
ordinates  are  spaced  so  that  addition  mostly  is  employed  to  find 
the  area.  The  number  of  ordinates  which  it  is  proposed  to  use 
having  been  selected,  the  subjoined  Table  gives  the  fractions  of 
the  half  length  of  base  at  which  they  must  be  spaced,  starting 
always  from  the  half  length.  The  ordinates  are  then  measured 
off  and  summed,  the  addition  being  divided  by  the  number  of  the 
ordinates.  giving  a  mean  ordinate,  which  multiplied  by  the  length 
of  base  produces  the  area  :  — 

Sum  of  ordinates      _  ,  , 

^—    -i rr-       -  x  Length  of  base  =  Area. 

>>o.    ot  ordinates 


22 


The   Naval   Constructor 


Tchibyscheff's  Ordinate  Table. 


Number 

OF  ()R- 

DISTANCE   OF    OUDINATES  FROM  MIDDLE 

OF  Base,  3£  ,  in 

DINATES. 

Fractions  of  Half  the  Base  Length. 

2 

.5773 

o 
o 

*  X,   -7071 

4 

.1870,       .7947 

5 

X,    -3745,       .8325 

6 

.2006,       .4225,       .8062 

< 

X,   -3239,     .5297,     .8839 

9 

3£,   .1079,     .5288,     .6010,     .9110 

10 

.0838,     -3127,     .5000,     .6873,     .9102 

The  employment  of  this  rule  to  find  the  volume  of  displace- 
ment and  the  other  elements  usually  tabulated  on  the  displace- 
ment sheet  is  shown  on  the  attached  Tables.  The  number  of 
stations  used  is  ten,  as  in  the  case  of  Simpson's  rule,  but  for 
clearness  the  after  body  five  are  indicated  by  Roman  numerals, 
and  the  fore  body  ones  in  Arabic.  The  displacement  length  is 
000  feet,  therefore  by  taking  the  fractions  given  in  the  preceding 
table  for  ten  ordinates  and  multiplying  them  by  300,  we  shall 
obtain  the  distance  of  the  displacement  sections  apart.  These 
distances  from  the  half-length  and  the  sections  are  here  given  as 
used  for  the  Table,  but  it  will  be  observed  that  the  water  lines  are 
spaced  to  suit  Simpson's  first  rule  for  the  vertical  sections  as  no 
advantage  would  be  gained  by  the  use  of  Tchibyscheff  in  this 
direction,  owing  to  the  fewer  number  of  water  lines  generally  neces- 
sary. The  various  operations  in  the  Table  will  be  clearly  under- 
stood from  the  headlines  of  the  respective  columns. 

As  already  pointed  out,  the  great  value  of  this  rule  is  in  the  cal- 
culations to  obtain  cross  curves  of  stability,  specimen  tables  of 
which  are  also  given.  The  fewness  of  the  sections  necessary,  and 
the  fact  that  the  integrator  saves  the  calculator  the  tedium  of  add- 
ing up,  tells  greatly  in  favor  of  the  adoption  of  this  rule  for  these 
calculations  both  as  a  time  saver  and  an  eliminator  of  the  chances 
of  error. 


T.  S.  S.  "L 


ucania 


>* 


23 


T.  S.  S.  "LUCANIA" 

BODY  SECTIONS  FOR  DISPLACEMENT  ETC.  BY     TCHIBYSCHEFF'S  RULE 
(for  CALCULATION  see  table) 


ORDINATES  FROM  AMIDSHIPS:- 
BEFORE       abaft 

1...A__I  ._  B     25.14 

2 4. H__  .=     93.90 

3--.A--  III--  =  150.00 

4 i. Vl._=  206.10 

5  ...  4 V =  2T4.80 


WATER-LINES  3.833'  APART 


Fig.  8. 


24 


The   Naval   Constructor 


Displacement  Sheet  by 


Stations. 

Water  Lines. 

1 

l 

2 

3 

4 

i 

5 

1 

t 

2 

1 

2 

I 

.00 
.15 

29.35 

20.35 

31.20 
23.40 

32.30 
64.60 

32.50 
32.50 
32.50 
32.50 

32.50 
65.00 
32.50 
65.00 

1 

.00 
.15 

29.35 

29.35 

31.20 
23.40 

32.25 
64.50 

II 

.00 

.15 

20.25 
26.25 

28.84 
21.63 

31.00 
62.00 

31.30 
31.30 

31.40 

62.80 

2 

.00 
.15 

25.00 
25.00 

27.35 

20.51 

29.25 

58.50 

30.00 
30.00 

30.20 
60.40 

III 

.00 
.15 

10.90 
1G.90 

20.85 
15.64 

19.85 
14.89 

24.00 

49.20 

20.55 
20.55 

27.85 
55.70 

3 

.00 

.15 

.00 

.15 

17.50 
17.50 

22.15 
44.30 

23.35 
23.35 

24.15 

48.30 

IV 

7.80 

7.80 

11.10 

8.33 

14.80 
29.60 

17.50 

17.50 
14.45 
14.45 

19.40 
38.80 

4 

.00 

.15 

7.00 
7.00 

11.15 
8.36 

13.20 
26.40 

15.35 
30.70 

V 

.00 
.15 

1.00 

1.00 

1.50 
1.13 

2.55 
5.10 

3.55 
3.55 

4.65 
9.30 

5 

.00 

.00 

.00 

.00 

.15 
.11 

2.20 

4.40 

3.10 
3.10 

3.65 

7.30 

Sum  of 
Ordinates 

5.40 

160.1* 

183.19 

204.30 

214.80 

221.65 

Functions 

1.35 

160.15 

137.38 

408.60 

214.80 

443.30 

Levers 

7.00 

0.50 
1,040.98 

6 

5 

4 

3 

Moments 

9.45 

824  28 

2,043.00 

859.20 

1,329.90 

Multipliers  for  Areas 

Areas  of 
Water 
Lines 

048.00 

19,218.00 

21,983.00 

24,516.00 

25,776.00 

26,598.00 

Divisor  for  Tons 

Tons  per 
Inch 

V= 

1.543 

45.70 

52.30 

58.371 

61.37 

63.29 

^.     .                          ,  .    ,       2  x  000  x  2  x  3.833 
Displacement  in  cubic  feet  —     —=- — =-^r-        x 
*                                                  3  x  10* 

D  = 

_.     ,                 .                          12x000x2x3.833 
Displacement  m  tons      .     . Qr     -  x 

|o  X   1U  X  oO 

A  =  Distance  of  Ordinates. 
*   10  =  number  of  stations.  t  3=  Simpsons'  multiplier. 


Displacement  Tables 


25 


Tchibyscheffs   Ri 

iile. 

Y  I  i:  I  h    \i    SE<   l  I-.N-. 

5 

>•■ 

7 

I'llllC- 

t  ion-. 

ItiH.r- 

<'l -. 

Levers. 

Mo- 
ments. 

1 

2 

h 

32.50 
32  50 

32.40 
64.80 

32  :;•'. 
16.1  - 

328.48 

.13 
13.60 

.0838 

.109 

32.50 
32.50 

31.45 

31.45 

32.40 
64.80 

32.30 

16.15 

328.35 

31.50 

i;:;.m 

31.45 
15.73 

314.31 

.313 

4.259 

30.25 

30.25 
28.55 

28.:..-, 

30.35 

60.70 

30.40 
15.20 

300.71 

29.10 
58.20 

29.25 

14.63 

265.52 

29.48 

.500 

14.740 

24.(i:, 
24.65 

l'5.10 

50.20 

25.40 
12.70 

236.04 

21.00 
21.00 

22.45 

44.90 

23.70 

11.85 

179.93 

34.24 

.687 

23.523 

16.10 

16  10 

16.90 

33.80 

17.45 

8.73 

145.69 

5.7") 
5.75 

6.90 

13.80 

8.25 
4.13 

43.91 

13.50 

.916 

12.367 

4.10 
4.10 

4.50 
9.00 

4.80 

2.40 

30.41 

226.85 

231.60 

235.35 

=  2i 
2,173.31 

Distance 

OF 

54.998 

226  85 

463.20 

117.68 

Wateb  Lines  =  3. 83:',' 

2 

1 

0 

453.70 

463.-J" 

o 

7,023.71 

of  Water  I 

jine- 

2. 

i  i  ntke  of  Buoyancy. 

27,222.00 

27, 792.00 

28,242.00 

7,023.71  x:;.833 

-12  39'|bel0W 

2.173.31 

■  1_-       \  W.L.  7 

per  Inch  : 

420. 

54998  -'  fi,,0  =  7..y..'  abaft  X 
2,173.31/  2 

64814 

66.171 

67.243 

2,173.31  = 

--  666,445.2 

5 

2,17331  = 

:  19,041.29 

24 


•  (3  -'.Oi+lOxOsj— 03)  =  Moments. 


ZiX',     <2=  Area  of  Water 
Lines.  2938 


26 


The   Naval   Constructor 


Center  of  Buoyancy  and 


&, 

Water 
Lines. 

°  A  a 
QQ 

H 

Hi 
1 

T 

Keel 

5.40 

W.L.  i 

160.15 

1 

W.L.  1 

183.19 

1 

W.L.  1 

183.19 

1 

2 

W.L.  2 

204.30 

2 

W.L.  3 

214.80 

i 

2 

W.L.  3 

214.80 

1 

W.L.  4 

221.65 

2 

W.L.  5 

226.85 

i 

2 

W.L.  5 

226.85 

1 

2 

W.L.  6 

231.60 

2 

W.L.  7 

235.35 

i 

2 

Prod- 
ucts. 


1.35 
160.15 

45.80 


207.31 

91.60 

408.60 

107.40 


814.90 
107.40 
443.30 
113.43 


1,479.03 
113.43 
463.20 
117.68 


2,173.34 


i) 


Mo- 
ments. 


80.07 
45.80 


125.88 

91.60 

817.20 

322.20 


1,356.87 
322.20 

1,773.20 
567.15 


4,019.46 
567.15 

2,779.20 
823.76 


8,189.57 


Formula. 


3.833  x  r 


125.87 


3.833  x 


3.833  x 


o.ooo  X 


207.31 


1356.87 
814.90 


4019.46 
1479.07 


8189.57 
2173.38 


C.B. 

ABOVE 

Keel. 


2.328 


6.383 


10.420 


14.450 


Displacement  in 

Keel    to    W.L.  1  : — x     207.31  = 

3  x  10 

„TT    ,       „rT   „       2X600X3.833 

W.L.  1  to  W.L.  2  :     — — x  2,335.55  = 

10  X  12 

_    .    .      ___  _     .     2  x  600  X  2  X  3.833 

Keel    to    W.L.  3:  - — x     814.90  = 

o  X  1(J 

3  x  600  x  2  x  3  833 

W.L.  1  to  W.L.  4  : ^ — —  x  1,662.14  = 

3X10 

Keel    to  WX,6:2X600X20X  3.833  xM79Q3  = 

W.L.  4  to  W.I,  6:       6°°  *  \  *  *™     x  1.360.65  = 

o  X   10 

rr    i  1TTT     ,     2X600X2    x.3.833 

Keel    to   W.L.  7  : — x  2,173.34  = 

o  X   10 


12 


A2 
X(5x0j  +  8X02—  03)  =  Area  by  f  rule.     —  X(3xOx  +  10x02—0..  =  Moments. 


Displacement  Tables  27 

Displacement,  by  Tchibyscheff s  Rule. 


7. 

-_ 


1 

2 
3 


1 
2 

3 
4 


4 
5 
6 


-I-    g     Pbod 

r.  ^  r- 


90 


183.10 
204.30 

214.80 


183.19 
204.30 

214.80 
221.65 


221.65 
226.85 

231.60 


l  >    I  3. 

2 


015.0.-) 
1634.40 

-214.80 


2335.55 

183.25 

612.00 

644.40 
221.65 


1662.14 

221.65 
907.40 
231.60 


1360.65 


3 

10 

1 


MO- 
MI  NTS. 


549  57 

2043.00 

-214.80 


I'<  >BM1   LA. 


C.B. 

\r.<>\  i. 
Keel. 


3.833  x 


2377.77 
2335.55 


i  i 


183.10 
1225.80 

1933.20 
886.60 


=    1.95 
3.833 

C.B.  of  W.L.-W.L.2=  ~5T783 

4.33 


2377    ~~  '"'  7SS  '  89621  63+2  328x63.'T4  52 


89521. 63+63574  62 

3.833  x  4228 


1662.14 

9.76X  286577.44+2.328  X  63574.52 


4228.70 

886.60 
4537.20 

i:>9.6<» 


286577.44+63574  52 


3.833  x 


6813.40 
1360.65 


'.'.70 
8.40 


=  10.20 


6813  40  19  "*  20861486  +  8-4X  350151.96  _ 

208614.86  +  350151.96      "  '--40 


Cubic  Fket  =  V 
63.574.52  1 

80,521.63 


-    .577.44 


208,614.86 


Cubic  Feet.  C.B.  Above  Keel. 

63,574.52  =  Keel  to  W.L.  1.  2.328 


153,096.15  =  Keel  to  W.L.  2. 


249,912.80=  Keel  to  W.L.  3. 


.  350,151.96  =  Keel  to  W.L.  4. 


453,558.21  =  Keel  to  W.L.  5. 


558,766.82  =  Keel  to  W.L.  6. 


1,445  24  =  Keel  to  W.L.  7 


4.33 

6.383 

8.40 

10.420 

12.4'. 

14.4--. 


Lever  =  A-  v  (3  X  °l  +  1°  X  °'~  °3>  —  A  v  (3  X  0l  +  1°  X  °»~0^ 
24  *  (5  X  0X  +  8  X  02  — 03)—  2  X  (5  X  0t+  8  X  0,  —  0J 


28 


The  Naval   Constructor 


Longitudinal  Metacenters  and  Centers 


Stations. 

I 

1 

II 

2 

III 

3 

IV 

4 

V 

5 

A 

2 

A 

2 

A 

2 

A 

2 

A 

2 

W.L.  7      .     . 

32.35 

32.30 

31.45 

30.40 

29.25 

25.40 

23.70 

17.45 

8.25 

4.S0 

A  respective 
2    .     .     .     . 

64.65 

1.05 

61.85 

3.85 

54.65 

6.25 

41.15 

3.45 

13.05 

Lever  respec- 
tive to  Lever2 

.084 

.007 

.313 

.008 

.50 

.25 

.687 

.472 

.916 

.840 

Moments 

.329 

1.925 

4.294 

3.160 

Moments  for 

I     .     .     .     . 

•  •  • 

.453 

.  .  . 

6.061 

•  •  • 

13.660 

•  •  • 

19.423 

.  .  . 

10.962 

W.L.  6      .     . 

32.40 

32.40 

31.50 

30.35 

29.10 

25.10 

22.45 

16.90 

6.90 

4.50 

A  respective 
2    .     .     .     . 

64.80 

1.15 

61.85 

4.00 

54.20 

5.55 

39.35 

2.40 

11.40 

Lever  respec- 
tive to  Lever2 

.084 

.007 

.313 

.098 

.50 

.25 

.687 

.472 

.916 

.840 

Moments 

.340 

2.00 

3.813 

2.198 

Moments  for 

I     .     .    .     . 

•  •  • 

.454 

.  .  . 

6.061 

•  •  • 

13.55 

.  .  . 

18.573 
16.10 

•  •  • 

9.576 

W.L.  5      .     . 

32.50 

32.50 

31.45 

30.25 

28.55 

24.65 

21.00 

5.75 

4.10 

A  respective 
2    .     .     .     . 

1.20 
.313 

61.70 
.098 

3.90 
.50 

53.20 
.25 

4.90 
.687 

37.10 
.472 

1.65 
.916 

9.85 
.840 

Lever  respec- 
tive to  Lever2 

.084 

.007 

Moments 

.376 

1.95 

3.366 

1.511 

Moments  for 

i 

I     .    . 

6.047 

.  .  . 

13.30 

| 

17.510 

.  .  . 

8.274 

W.L.  4      .    . 

32.50 

32.50 

31.40 

30.20 

27.85 

24.15 

19.40 

15.35 

4.65 

3.65 

A  respective 
2    .     . 

1.20 

61.60 

3.70 

52.00 

4.05 

34.75 

1.00 

8  30 

Lever  respec- 

tive to  Lever2 

.084 

.007 

.313 

.098 

.50 

.25 

.687 

.472 

.916 

.840 

Moments 

.376 

1.850 

2.782 

.916 

Moments  for 

I     .     .     .    . 

•  •  • 

•  •  • 

6.037 

•    •      • 

14.00 

...| 

16.400 

.  .  . 

6.972 

A  =  Difference.  2  =  Sum. 

23  =  Sum  of  Moments  (Sums  x  lever2)  for  I. 


Displacement  Tables 


29 


of  Flotation,  by  Tchibyscheff s  Rule. 


2  "1 

MOMKN  !  S. 

Ckntkr 
aktX 

«  £ 

/ 

|  AXIS  —  hL 

BETWKES 

r.p.) 

I » i:  i  •  i  <  piOM 
Akka  W.L. 

Xa^. 

V 

V 

A 

5 
- 

5 
- 

10 

=10,800,000  2, 

546.900.000 

28,242x12.09" 

4.128,000 

666,445 
542,772,000 

Lon- 
gitu- 
dinal 

R.M. 
in  Ft 

312.93 

9.708 

50.559 

235.35 

12.09 

27,792xl0.8132 
3,249.440 

558,767 
517.461,760 

926.07 

8.351 

-    214 

8351X   ^ 
8,301  X23T60 

.... 

10.813 

• 

27,222  ■    9.525 
2,469,715 

•  ■ 

453,558 

•  ■          • 

484,945,085 

1069.2 
1334.0 

45.131 

.... 

9.525 

4>7.414.800 

26,598  X  8.0182 
1,709, 

•          •         • 

350,1. -.2 

•     '     • 

167,107 

5.924 

•     ■     • 

13.409 

W>24>  -3ft0 

8.018 

.... 
468,817,200 

2]  =  Sum  of  Ordinates  on  Displacement  Table. 

2)  =  Sum  of  Momenta  (differences  x  lever)  fur  Centers  of  Flotation, 


30 


The  Naval   Constructor 


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Explanation   ot   Table  31 


EXPLANATION    OF    TABLE,    GIVING    EFFECT    OF 

FORM    OF    WATER    LINE     ON    POSITION 

OF   LONGITUDINAL    METACENTER. 

Longitudinal  and  Lateral  Stability  Compared.  —  The 
first  four  lines  are  exactly  the  same  a-  those  in  the  other  table  ; 
and  the  last  eight  lines  differ  only  in  having  length  and  breadth 
interchanged,  bo  as  to  give  pitching  instead  of  rolling. 

On  comparing  them  with  the  following  table,  it  will  be  noticed 
that,  in  the  algebraic  factor,  the  length  and  breadth  always  inter- 
change ;  and  that  the  numerical  factor  remains  unchanged  for 
forms  (1).  (3),  and  (A),  namely,  the  square  or  rectangle,  the 
circle  or  ellipse,  and  the  wedge.  Of  the  nine  forms  selected,  these 
are  obviously  the  only  ones  in  which  breadth  and  length  are 
absolutely  interchangeable. 

With  respect  to  the  comparison  of  the  different  forms,  one  with 
another,  if  we  disregard  the  wave-bow  No.  (8),  the  variation  of 
stability  follows  much  the  same  sequence  for  longitudinal  as  for 
lateral  stability,  but  with  a  somewhat  less  absolute  value.  This 
result  might  be  expected  a  priori,  because  the  extreme  breadth 
ordinate  cuts  the  outline  at  right  angles  in  all  but  the  wedge 
form  (9)  ;  while  the  extreme  length  ordinate  meets  the  outline 
more  sharply.  In  forms  (2)  and  (4)  this  difference  is  only  of 
the  second  order  ;  but,  as  the  figures  show,  it  is  quite  sufficient  to 
be  of  practical  importance  even  in  these. 

Differ  Chiefly  in  Wave-Bow.  —  The  wave-bow  form  (8) 
falls  altogether  out  of  its  sequence,  and  its  stability  is  less  than 
the  wedge  form  (0)  as  regards  pitching.  This  is  due  to  the 
sudden  falling  off  of  the  extreme  ordinate  length,  which  meets 
the  curve  tangentially,  instead  of  normally,  as  the  extreme 
breadth  ordinate. 

Fine  Bow  Affects  Pitch  More  than  Rolling.  —  If  we 
consider  rolling  on  any  given  axis,  it  is  easily  seen  from  geometri- 
cal considerations,  and  also  from  the  algebraic  form  of  the  inte- 
gral, that  the  instantaneous  stability  depends,  firstly,  on  the  length 
of  the  transverse  axis,  and,  secondly,  on  the  slowness  of  the  rate 
of  diminution  of  that  axis,  as  we  pass  along  that  axis  of  motion. 
Hence  sharp  bows  have  less  stability  for  pitching  than  bluff  bows, 
while  their  lateral  stability  for  rolling  i*  not  so  very  different. 

Caution  in  Use  of  Table.  —  In  the  table  of  lateral  stability, 
the  element  of  length  only  appears  as  a  simple  factor  ;  therefore, 
as  regards  lateral  stability,  we  may  compound  the  moments  by 


32  The   Naval  Constructor 


simple  addition  for  a  vessel  built  up  in  different  lengths  for  the 
different  forms.  Thus,  the  values  in  lines  1  to  8  of  column  (2)  are 
simply  the  means  of  the  corresponding  values  in  columns  (1)  and  (3). 
We  cannot  apply  this  process  to  the  longitudinal  stability  because 
here  the  length  element  enters  as  a  cubic  factor.  If  we  were  so  to 
compound  the  moments  of  length,  what  we  should  really  do  would 
be  equivalent  to  screwing  together  two  longitudinal  halves  of 
different  vessels  ;  in  the  case  before  mentioned,  screwing  half  a 
box  to  half  a  tub  ;  not  introducing  a  flat  midship  length  between 
two  semicircular  ends. 


Effect  of  Form  of  Water  Line  33 

Explanation  of  Table  Giving  Effect  of  Form  of  Water 
Line  on  Position  of  Metacenter. 

Explanation  of  Table.  —  By  the  preceding  table  we  can  at 
once  make  an  approximate  estimate  of  the  value  of  any  proposed 

form  of  water  line,  by  selecting  that  form  in  the  table  to  which 
it  comes  nearest.  From  this  table  we  gather  that  the  more 
nearly  the  water  line  approaches  to  a  right  parallelogram,  the 
more  it  will  contribute  to  the  stability  of  a  ship.  No.  9,  on  the 
contrary,  the  straight  line  wedge  form,  is  the  least  stable  of  these 
water  lines,  and  from  the  comparison  of  the  successive  groups  of 
lines  on  the  table  we  shall  see  exactly  how  this  comes  about. 

Areas  on  Water  Lines.  —  The  first  and  second  lines  in  the 
table  give  the  measures  simply  of  the  areas  of  those  water  lines. 
From  lines  3  and  4  we  see  that,  Fig.  1  being  taken  as  the  stand- 
ard of  comparison,  Fig.  2  only  contains  89  per  cent  of  the 
rectangular  area,  and  this  diminution  is  effected  merely  by  round- 
ing off  the  rectangular  corners,  the  length  and  breadth  remaining 
the  same  in  both.  In  Fig.  3,  when  the  curvature  of  the  ends 
extends  quite  to  the  middle  of  the  water  line,  its  area  is  reduced 
to  69  per  cent.  In  Fig.  6,  by  forming  the  water  line  of  parabolic 
arcs,  a  favorite  form  of  some  builders,  the  area  is  reduced  to  two- 
thirds  of  the  rectangle.  Figs.  7  and  8  are  the  lines  used  for 
a  wave  stern  and  a  wave  bow  ;  from  which  it  appears  at  once 
how  much  more  powerful  the  stern  contributed  to  the  stability  of 
a  ship  than  the  bow  ;  the  stern  line  being  62  per  cent,  and  the 
bow  line  only  50  per  cent. 

Metacentric  Moments.  —  Lines  5  and  6  are  the  actual 
measure  of  the  stability  (by  its  moments)  for  small  inclinations. 
For  example  :  in  the  rectangle,  the  moment  is  one-twelfth  part  of 
the  product  of  the  length  by  the  cube  of  the  breadth,  or  .08  of 
that  product ;  and  as  we  pass  along  line  6  we  find  it  gradually 
diminish,  until,  in  the  wedge  form,  it  is  only  .02,  showing  that  a 
sharp  wedge  form  has  only  one-fourth  part  of  the  power  to  carry 
top  weight  that  the  rectangular  form  has,  although  its  power  of 
buoyancy,  or  power  to  carry  absolute  load,  is  one-half.  This  is 
set  out  more  fully  in  lines  7  and  8  ;  so  that  by  carefully  comparing 
together  line  4  and  line  8.  the  relative  values  of  all  those  figures 
for  carrying  absolute  weight  and  for  carrying  top  weight  may  be 
clearly  seen. 

Metacentric  Intervals.  —  Lines  9  and  10  measure  the 
powers  of  ships,  formed  on  these  water  lines  only  to  carry  top 
weight  without  upsetting. 


34 


The   Naval   Constructor 


Effect  of  Form  of  Water  Line  on 

From  J.  Scott  Russell, 
Length  of  vessel  =  L*  Breadth  on  water  line 


s  o 

-  H 

-  -^ 


1  Area  of  plane  of  flotation  . 

2  The  same,  expressed  decimally 

3  Ratio  to  same  in  rectangular  \ 

form ) 

4  The  same,  expressed  decimally 
oJlxMyj 

G  The  same,  expressed  decimally 

7  Ratio  to  same  in  rectangular  ( 

form ) 

8  The  same,  expressed  decimal!  y 

9  Height  of  longitudinal  meta- 

center  above  center  of  dis- 
placement % 


LB 
LB 


10  The  same,  expressed  decimally?. 

11  Ratio  to  same  in  rectangular  | 

form  % J 

12  The  same,  expressed  decimally:; 


L3B 
LSB 


L* 

dr~. 

Z2 
dr. 


(1) 


si 

GQP3 

[fflv! 


i 

1.00000 

1 

1.00000 

12 
0.08333 

1 

1.00000 

1_ 

12 

0.08333 

1 

1.00000 


(2) 

-•■-  - 

?  2  *  ; 

BOS  S 


4   -f-  7T 

_ 8~ 
0.89270 

4  +  7T 

8 

0.89270 

1G  +5tt 
512"- 

0.06194 

48  4-  15tt 
128 

0.74340 

16  +  5  77 


16(16  +  4tt) 

0.06937 
3(16  +  57r) 


4  (16  -4-  4tt) 


0.83248 


(3) 

o 

SI  J 


0.78540 


1* 


0.78540 


sV 


0.04909 


3    . 

IB  ' 


0.58905 


is' 


0.06250 


It 


0.73000 


*  The  length  i  appears  simply  as  a  factor.  The  numerical  factor  in  the 
table,  therefore,  remains  unchanged  if  the  proportion  of  L  to  B  be  altered, 
as  in  passing  from  the  square  to  the  rectangle,  or  from  the  circle  to  the 
ellipse. 

t  That  is  to  say,  a  trochoid  twice  the  length  of  a  cycloid  of  the  same  width. 


Effect  of  Form   ot  Water   Line 


35 


Position  of  Longitudinal  Metacenter. 

Nav.  Arch.,  isii:>, 

amidships  —  Ji.  Draught  of  water  =  dr. 


Ni 

MKltKAL   FACTOB    Kdlt 

(4) 

(5) 

(6) 

(7)t 

(8) 

(9) 

Cycloid  (a 
Pull  Wave 

Stern). 

u  *» 

-  S  — 

-»  is 

a  -  3 
s-  ti  - 

25  ~  C 

I 

C   DO  ~   go 

Troclioid 

1  :  2 

(a  Wave 

Stern). 

Curve  of 

Sines  ct 
Wave  En- 
trance). 

o> 

<£> 

<^> 

<& 

<s> 

<£> 

3 

TT  —  2 

2 

5 

1 

1 

4 

<KV2  - 1) 

3 

8 

2 

2 

(1.75000 

0.68901 

0.C6i!7 

0.62500 

0.50000 

0.50000 

3 

4 

IT  —  2 

2 

3 

5 

8 

1 
2 

1 

2 

•i(V-'-i) 

0.75000 

0.68901 

0.66667 

0.62500 

0.50000 

0.50000 

12rr2  —  35 

3tt  — 8 

1 

80tt2  —  373 

7T2—   6 

1 

192  nn- 

96  V2  —  1 

30 

1536  7r2 

24  rr2 

48 

0.04403 

0.03583 

0.03333 

0.02748 

0.01634 

0.02083 

12tt2  —  35 

3tt  —  8 

2 

80tt2  —  373 

TT2  —   6 

1 

16  tt2 

8V2  -  1 

5 

128  TT2 

2rr2 

4 

0.52836 

0.4299G 

0.40000 

0.32974 

0.19604 

0.25000 

12tt2  —  35 

3tt—  8 

1 

80tt2  —  373 

7T2—    6 

1 

144  TT2 

24   n       2 

20 

960  77- 

12    7T- 

24 

0.05871 

0.05200 

0.05000 

0.04397 

0.03267 

0.04167 

12tt2  —  ::.-, 

3tt 

3 

30irJ  -  -  373 

TT2-       8 

1 

12  77" 

2(W-'2) 

5 

■SO  rr2 

77 '- 

2 

0.70446 

0.62403 

0.60000 

0.52759 

0.39207 

0.50000 

t  The  entries  in  these  lines  assume  thai  the  vessel  is  flat-bottomed,  with 

vertical  sides.  The  other  entries  hold  good  whatrver  may  he  the  shape  of 
the  vessel  underwater.  In  general,  the  height  of  the  metacenter  maybe 
found  by  dividing  the  entry  in  lines  5  or  6  by  the  displacement. 


36 


The   Naval   Constructor 


Effect  of  Form  of  Water  Line 


Length  of  vessel  =  L.* 


From  J.  Scott  Russell, 
Breadth  on  water  line 


1  Area  of  plane  of  flotation  J    . 

2  The    same,    expressed    deci-  ^ 

mally  % | 

3  Ratio  to  same  in  rectangular  ) 

form ) 

4  The  same,  expressed  decimally 
bjlyhlxt 

6  The  same,  expressed  decimally} 

7  Ratio  to  same  in  rectangular  ( 

form | 

8  The  same,  expressed  decimally 

9  Height  of  metacenter  above  \ 

center  of  displacement  §      .  j 

10  The    same,    expressed    deci- ) 

mally  § I 

11  Ratio  to  same  in  rectangular  \ 

forms | 

12  The  same,  expressed  decimally§ 


o 

<  £ 

a  h 

■-  < 


LB 
LB 


LB* 
LB3 


B* 
dr. 

J?! 
di\ 


(1) 

-he 


1 
1.00000 

1 

1.00000 

1 

12 

0.08338 

1 
1.00000 

_1 

12 

0.08333 


1.00000 


(2) 


•„  »^  to 
ogCfi  3-0 

s  -1  u  a 

(HB 


™8~~ 
0.89270 

4+7T 

8 
0.89270 

16  +  37T 

384 

0.0G621 

16-4-3tt 
32 

0.79452 

16  +  3tT 


12(16+4  77) 
0.07417 

16  +  37T 
16  +  47T 

0.89003 


(3) 


sag 


0.78540 


1* 


0.78540 


E-i 


0.04909 


3  . 

is  ' 


0.58905 


1  . 


0.06250 


0.75000 


*  The  length  L  appears  simply  as  a  factor.  The  numerical  factor  in  the 
table,  therefore,  remains  unchanged,  if  the  proportion  of  L  to  B  be  altered, 
as  in  passing  from  the  square  to  the  rectangle,  or  from  the  circle  to  the 
ellipse. 

t  That  is  to  say,  a  trochoid  twice  the  length  of  the  cycloid  of  the  same 
width. 


Effect  of  Form   of  Water   Line 


37 


on  Position  of  Metacenter. 

X'ir.   .irrlt.,   18 
amidships  =  B.  Draught  of  water  =  «lr. 


Xl.MKKIi    \\. 

Factor  fob 

(4) 

(5) 

(6) 

■ 

•       (8) 

Cycloid  (a 

Pull  Wave 

Stern). 

-  -  c 

»  —  z 

-  -  i 

Parabola 

(Axis 

Athwart- 

sliijisi. 

Trochoid 

1  :  2 
(a  Wave 

.St. Tin. 

-  —  i 
-  /.  .    •_ 

r  S  Z-  - 
-=  33  >  z 

6 

— 

s 

<2> 

<£> 

<r> 

€> 

<©> 

<I> 

3 
4 

IT  —  2 

2 
3 

5 

8 

l 

2 

1 

2 

4(V2-1) 

0.75000 

0.68901 

0.6667 

0.6250 

0.50000 

0.50000 

3 
4 

IT  — 2 

2 
3 

5 

8 

1 
2 

1 

•j 

4  (V2  - 1) 

0.75000 

0.68901 

0.6607 

0.62500 

0.50000 

0.50000 

35 

1         9  TT  —  28 

4 

55 

5 

1 

768 

24    20V2—  28 

105 

1536 

1,2 

4- 

0.04557 

0.04021 

0.03810 

0.03581 

n.ir_'|]08 

0.02083 

35 

1      9tt  —  28 

16 

55 

6 

1 

64 

2     20V2— 28 

35 

128 

10 

4 

0.54688 

0.48252 

0.45714 

0.42969 

0.31250 

0.25000 

35 

2 

11 

5 

1 

57  G 

35 

96 

•J4 

0.06076 

0.05836 

0.05714 

0.05729 

0.05Ji>s 

D.O4107 

35 

24 

11 

5 

1 

48 

* 

35 

16 

8 

2 

0.72917 

0.70031 

0.68571 

0.68750 

0.62500 

0.50000 

+  These  are  all  areas  or  moments,  and  therefore,  for  compound  forms,  it 

is  only  necessary  to  add  them,  or  take  a  mean  of  them,  as  may  suit  the  par- 
ticular case. 

§  The  entries  in  these  lines  assume  that  the  vessel  is  flat-bottomed,  with 
vertical  sides.  The  other  entries  hold  good,  whatever  may  be  the  shape  of 
the  vessel  under  water.  In  general,  the  height  of  the  metacenter  may  be 
found  by  dividing  the  entry  in  lines  5  or  6  by  the  displacement. 


38  The   Naval   Constructor 


Modulus  of  Fineness.  —  Lines  11  and  12  enable  us  to  com- 
pare the  different  forms ;  and  by  running  our  eye  along  line  12 
we  are  enabled  to  trace  the  effect  of  the  successive  changes  in  the 
form  of  water  line,  in  bringing  down  the  metacenter,  and  re- 
ducing the  stability  of  the  ship,  thus  giving  what  has  been  some- 
times called  the  modulus  of  fineness  of  water  line. 

STABILITY    CALCULATION,  USING    THE 

INTEGRATOR   AND    APPLYING 

TCHIBYSCHEFF'S    RULE. 

The  following  tables  will  show  the  application  of  the  above  rule 
to  the  calculation  of  the  stability  levers  GZ  from  the  body  plan 
reproduced,  noting  that  the  integrator  used  was  metrically 
divided,  and  the  original  drawing  was  to  a  scale  of  •§•  to  the  foot  or 
^g-  full  size  with  ten  Tchibyscheff  ordinates.  The  center  of 
gravity  was  assumed  at  24  feet  above  base.  The  coefficients  are 
therefore  as  follows,  the  length  of  vessel  being  600  feet :  — 

For  displacements  (tons), 

600      962  x  3.2812      ,„_  _ 
To*     100X35     =1'01-6- 
For  levers  (feet), 

.06  x  96  X  3.281  =      18.9. 
and, 

Displacement  in  tons  = 

1701.5  x  sum  of  differences  of  area  readings. 

.     .  18.9  X  sum  of  differences  of  moment  readings 

Levers  in  feet  = — .   ,._- 2 —. — ■  • 

Sum  of  differences  of  area  readings 

or, 

Displacements  (D)  =  1701.5  x  I    }  I  respective  to  II  taken  up 

,  _,_  ,,«  «      JZ?  to  the  corresponding  water 

Levers  {GZ)  =      18.9  x  -  ^ineg> 

The  angles  calculated  were  15°,  30°,  45°,  60°,  75°,  and  90°,  and 
the  results  as  tabulated  used  to  plot  off  the  Stability  Cross  Curves 
shown  from  which  the  Stability  Curves  at  various  displacements 
were  taken,  the  correction  being  calculated  for  the  new  locii  of 
the  center  of  gravity  where  G  is  the  assumed  position  below  S  then 
GZ  =  SZ  +  SG  sin  0,  and  when  above  S  then  GZ=SZ-SG  sin  6. 
So  that  taking  the  ordinates  from  the  cross  curves  at  the  displace- 
ment dealt  with  SG  being  now  known,  we  can  determine  the  exact 
values  of  GZ  for  any  angle. 


Stability   Calculations 


39 


TCHIBYSCHEFF  SECTIONS, FOR  STABILITY  LEVERS  G.  Z. 
SEE   TABLES 


S< 


Fig.  9. 


40 


The   Naval   Constructor 


Calculation    of 
Using  the 


GZ   Levers   for  Stability  Cross    Curves, 
Integrator  and  Tchibyscheffs  Rule. 


1 
it 

A  £ 

i-C  l"H 

a  o 

'A  H 
H 

SB 

Area 
k.   Read- 
ings. 

Differ- 
ences of 
|  Readings. 

Sum  of 
k,  Differ- 
ences. 

HI  M 

ce  «  *r 

Moment 
i§;    Read- 
ings. 

Differ- 
ences of 
Readings. 

^  fa  w 
g  fa  o 

5  fa  z 

6  -i  7\ 

II 

&.  i 

n  r  s 

H   fa 

cc  ^ 
GZ 

4555 

4511 

5 

7666 
7666 

3111 

3.111 

5,290 

5097 
5097 

+.586 

+.586 

3.56U 

4 

9668 
9668 

2002 

5.113 

8,700 

4931 
5169 

-.166. 

+.420 

1.550 

o 
I— 1 

3 

1779 

2111 

7.224 

12,280 

4974 

-.195 

+.225 

.590 

1779 

5211 

2 

3896 
3896 

2117 

9.341 

15,900 

5141 

5378 

-.070 

+  155 

.314 

L.W.L. 

6115 
6115 

2219 

11.560 

| 

19,700 

5423 
5661 

+.045 

+  200 

.327 

L.W.L. 

7685 

.  .  . 

11.570 

.  .  . 

5863 

.  .  . 

+  202 

Check 

0625 

5060 

5 

3766 
3766 

3141 

3.141 

5,350 

5820 
6079 

+.760 

+.760 

4.570 

4 

5578 
'5578 

1812 

4.953 

8,440 

6122 

6380 

+.043 

+.803 

3.070 

o 

3 

7681 

2103 

7.056 

12,000 

6317 

-.063 

+.740 

1.980 

o 

7681 

6575 

2 

9980 
9980 

2299 

9.355 

15,920 

6525 

6784 

-.050 

+.690 

1.395 

L.W.L. 

2411 
2411 

2431 

11.786 
| 

20,050 

6963 
7221 

+.179 

+.869 

1.386 

L.W.L. 

4201 

.  .  . 

11.790 

.  .  . 

8091 

.  .  . 

+.870 

Check 

8309 

9862 

5 

1620 
1620 

3.311 

3.311 

5,640 

0549 
0549 

+.687 

+.687 

3.930 

4 

3412 
3412 

1792 

5.103 

8,680 

0820 
1056 

+.271 

+.958 

3.550 

o 

3 

5519 

2107 

7.210 

12,250 

1411 

+.355 

+1.313 

2.950 

o 

5519 

1647 

2 

7874 

7874 

2355 

9.565 

16,300 

1999 
2235 

+.352 

+1.665 

3.260 

L.W.L. 

0365 
0365 

2491 

12.056 

| 

20,400 

2463 

2699 

+.228 

+1.893 

2.970 

L.W.L. 

2423 

•  •  • 

12.058 

1.896 

Check 

Calculation   of  GZ 


41 


Calculation    of 
Using  the 


GZ    Levers    for    Stability    Cross    Curves, 
Integrator  and  Tchibyscheff's  Rule. 


-  : 
— 

tU       IvIlAD- 
IN(iS. 

3  & 

rr  oe  — 

*  _  p 

-  -  - 

-   i 

-  -  i 

—  «  - 

f.    :      - 

a  S  S? 

QG  ~  H 
/ 

i 

—   — . 
— 
D 

i  a  y 

<-• 

.'.  -  a 

~   _  ^ 
~  *  - 

i 

mm     "^    ' 

c  ~  * 

•/.  c  - 
II 

00 

—  -~  !Z 
J.     .2 

<;z 

6007 

4860 

5 

usns 

i.Sl.s 

3711 

3.711 

6,315 

5547 

5547 

+.678 

+.678 

3.46 

4 

1684 
1684 

1876 

."..587 

9,620 

6051 

6285 

+.504 

+1.182 

4.00 

o 

3 

3746 

2062 

7.640 

13,000 

6637 

+.352 

+1.534 

3.80 

o 

3746 

6871 

2 

5076 
5976 

2230 

9.879 

1C.800 

7186 

7420 

+.315 

+  1.81!' 

3.50 

L.WX. 

8241 
8241 

226^ 

12.144 

I 

20,550 

7514 
7778 

+.124 

+1.073 

3.07 

L.W.L. 

0380 
0622 

.  .  . 

12.148 

.  .  . 

0754 
1355 

.  .  . 

+1.076 

Check 

5 

4832 
4832 

4210 

4.210 

7,160 

2078 
2078 

+.723 

+.723 

3.25 

4 

6676 
6676 

1844 

6.054 

10,300 

2448 
2020 

+.370 

+  1.003 

3.42 

o 

3 

8500 

1923 

7.077 

13.600 

3166 

+.246 

+1.339 

3.18 

1  . 

8500 

3402 

2 

0680 
0680 

2000 

10.067 

17,130 

3503 

3740 

+.101 

+1.440 

2.70 

L.W.L. 

2860 
2860 

2171 

12.238 
| 

20,800 

3800 

4i:;: 

+.150 

+1.-.00 

2.46 

L.W.L. 

5000 

.  .  . 

12.230 

.  .  . 

0 1  o  i 

.  .  . 

+1.600 

Check 

0521 

5800 

5 

6039 

5030 

4518 

4.518 

7,ooo 

6332 
6332 

+.442 

+.442 

1.85 

4 

6783 

1741 

6.262 

10,560 

6438 
6674 

+.1(10 

+.548 

1.66 

o 

3 

8637 

1854 

8.116 

13,810 

6767 

+.003 

+.011 

1.40 

_ 
- 

8637 

7004 

2 

0(585 

2048 

10.164 

17,295 

7128 
7364 

+.121 

+.70.-, 

1.42 

L.W.L. 

2880 
2880 

2195 

12.359 

1 

21,030 

7436 

7072 

+.072 

+.837 

1.20 

L.W.L. 

5242 

.  .  . 

12.362 

.  .  . 

8511 

... 

+.830 

Check 

42 


The   Naval   Constructor 


3 

P=4 


I  I  I  I  II  I   I  I  I  I   I  I  I   I  I   I  I  1   I   I  I 


J.333    SU3A3T  dO  31V33 


Cross   Curves  of  Stability 


43 


44  The   Naval   Constructor 

CHAPTER   II. 

DESIGN. 

In  the  foregoing  pages  we  have  treated  with  the  various  calcula- 
tions which  confront  the  naval  architect,  but  the  relation  of  these 
to  one  another  and  to  the  particular  qualities  that  the  projected 
ship  shall  possess  belong  to  Design. 

In  designing  the  ship,  nothing  should  be  left  to  chance,  or  what 
is  the  same  thing  —  trial  and  error.  The  vessel  must  first  be  de- 
signed with  figures.  Before  a  single  line  is  run  on  paper,  the  vari- 
ous element  coefficients  should  be  carefully  selected  and  their 
functions  worked  out  in  consonance  with  the  results  desiderated 
in  the  finished  ship.  The  relation  of  these  coefficients  to  one 
another  must  be  firstly  mastered  for  all  types  of  vessels  and  con- 
ditions of  draught  and  trade,  when  with  the  aid  of  the  tables  given 
an  unerring  selection  will  be  possible  and  a  definite  result  attained. 

When  the  way  is  prepared  for  the  drawing  part  of  the  design  to 
be  taken  in  hand,  it  will  be  found  advantageous  to  have  a  definite 
routine  in  which  to  prepare  the  various  views  comprised  under 
the  general  term  "Lines."  Each  step  should  be  taken  in  its 
proper  time  and  order.  Much  time  will  thus  be  gained,  and  a 
clearer  conception  of  the  art  of  designing  obtained.  To  this  end 
we  submit  the  following  method  as  one  fulfilling  these  proposi- 
tions, dividing  the  task  broadly  into  two  parts,  viz.  :  — 

(a)  Figures  aud  (6)  Lines,  the  first  embracing  the  moulded 
dimensions,  draught,  element  coefficients,  and  their  functions,  and 
the  latter,  the  sheer  draught,  half-breadth,  and  body  plans. 

The  shipowner  will  specify  the  trade  for  which  the  ship  is  in- 
tended and  the  limit  of  draught  on  the  particular  service  proposed. 
It  will  generally  be  found  economical  to  take  advantage  of  the 
maximum  draught  permissible.  When  the  dimensions  are  solved 
to' meet  the  requirements  stipulated,  the  grade  numerals  should  be 
worked  out,  for  the  Classification  Society's  Rules  in  which  it  is 
proposed  to  class  the  ship,  and  if  it  be  found  tbat  a  grade  can  be 
saved  either  in  plating,  framing  or  equipment  numerals,  or  the 
requirements  for  extreme  proportions  evaded  by  a  slight  alteration 
or  adjustment  of  the  dimensions,  this  of  course  should  be  done. 

As  an  example  we  shall  postulate  that  the  shipowner  requires  a 
3-deck  freighter  with  complete  shelter  deck  to  carry  10,000  tons 
dead  weight,  exclusive  of  coal  for  12  days'  steaming,  fresh  water 
and  stores,  on  a  mean  draught  of  27  feet  with  a  B.T.  Freeboard 
and  a  sea  speed  of  12  knots.  The  ship  to  be  classed  in  American 
Record  and  to  conform  to  the  U.S.  Inspection  Laws.     To  these 


Design  45 


demands  of  the  owner  the  naval  architect  should  add  the  G.M.  when 
fully  loaded  with  a  homogeneous  cargo.     Let  us  call  this  1.6  ft. 

The  first  point  to  determine  is  the  amount  of  displacement  we 
shall  require  to  provide  for  over  and  ahove  the  specified  dead 
weight  of  10.000  tons,  to  allow  for  weight  of  finished  ship  and 
machinery,  coal,  fresh  water,  and  stores.  At  this  stage  we  cannot 
calculate  these  items,  as  we  are  uninformed  as  to  the  dimensions 
of  the  ship,  so  that  the  remaining  method  to  solve  this  is  to  esti- 
mate a  weight  embracing  all  of  these  items  based  on  a  percentage 
of  the  dead  weight.  This  percentage  of  course  is  determined  from 
vessels  of  similar  type  and  trade  duly  worked  out  and  tabulated 
by  the  naval  architect.  We  shall  take,  then,  each  step  in  its 
proper  order  : 

(1)  Displacement  =  dead  weight  X  1.64  =  16,400  tons. 

(2)  Block  coefficient  "5"  =  a.p  e.  =  .79. 

s 

(3)  Relation  coefficient  "e"  =        =  .945.* 

a./i 

(4)  Mid.  area  coefficient  "/S"  =  — =  .i>7. 

a.e 

(5)  Prismatic  coefficient  "p  "  =  -  =  .814. 

(6)  Area  of  L.W.L.  coefficient  "  a  "  =  -  =  .861. 

(7)  Moment  of  inertia  coefficient  "i"  (see  table)  =  .0638. 

(8)  B.M.  coefficient  "m"=^=.08. 

n 

(0)    Center  of  gravity  coefficient  "  g  "  =  —  = . 550.     (See  table. ) 

(10)  Depth  "  H "  to  upper  deck  per  Freeboard  Tables  =  33.5  ft. 

(11)  Depth  "flx"  to  shelter  deck  =  H+  7.5  ft.  =  41  ft. 

(12)  Center  of  gravity  above  base  =  HlXg  =  ±\  X.659  =  22.00  ft. 

(13)  Metacenter  above  base  =  C.G.  +  G.M. 

=  22.1)0  +  1.50  =  24.40  ft. 

(14)  Breadth  "5"  to  give  M.C.  of  24.4  ft.  = 


\  *-'  Ps5) 


<  —  =  58.5  feet, 
m 

(15)    Length  "  L-.=_r_  =  m  ft. 

(X6)B.M.  =IXfXi4  =  Mf, 

(17)    Center  of  buoyancy  above  base 

.  /5a—  25 \       ,  .     „  . 

•  May  be  taken  constant  .9,  as  per  table. 


46  The  Naval  Constructor 

(18)  Bilge  diagonal  coefficient  (see  diagram)  =  .82. 

(19)  Dimensions  as  determined  =  400  x  58'  6"  x  33'  6". 

(20)  Displacement  "D" 

400' x  58.5' x  27'       „_ 
= jr= x  .79  =  10,400  tons. 

CO 

(21)  Calculated  weights  : 

Hull  complete       ....  4,070  tons 

Machinery 730     u     (4,000  I. H. P.) 

Coal 750     "     (for  12  days) 

Fresh  water 200     " 

Stores 50     " 

0,400     " 
Dead  weight 10,000     " 

Displacement  =  10,400  tons 

Should  it  be  found,  however,  that  the  weights  calculated  for  the 
dimensions  as  worked  out  are  lighter  than  anticipated  when  we 
started  with  the  04  per  cent  of  the  dead  weight,  the  length  should 
be  reduced  accordingly.  On  the  other  hand,  if  the  weights  be 
excessive,  the  length  must  be  increased.  The  length  is  the  only 
dimension  that  should  be  adjusted,  as  it  is  the  one  factor  which 
has  no  vital  relationship  to  the  element  coefficients,  as  it  will  have 
been  noticed  that  the  primary  quality  aimed  at  was  the  G.M.  as  a 
measure  of  the  ship's  initial  stability  ;  and  as  the  center  of  gravity 
varies  with  the  depth,  so  the  metacentric  height  is  dependent  on 
the  breadth  and  draught. 

For  the  preliminary  design  it  will  be  sufficiently  close  to  esti- 
mate the  machinery  weights  on  the  I.H.P.  required,  and  for 
ordinary  merchant  practice  the  power  may  be  calculated  fairly 
accurately  by  the  Admiralty  constant  with  the  formula  :  — 

T.H.P.=^X^3    * 
C 

We  then  have  for  the  present  example,  with  constant  =207,  speed 
12  knots,  and  displacement  10,400,  an  indicated  horse-power  =4000. 
By  referring  to  the  table  given  elsewhere,  it  will  be  found  that  for 
twin  screw  freight  steamers  with  this  speed  that  the  I.H.P.  per 
ton  of  engine  boilers  and  water  equals  about  5.5,  so  that  we  get 
for  a  total  machinery  weight 

4000  TOA   * 

— —  =  730  tons. 

The  displacement  and  coefficients  should,  in  all  cases  of  steel 
steamers,  be  calculated  to  the  moulded  line  of  frames,  the  excess 
water  displaced  by  the  shell  plating,  amounting  to  about  1%,  being 
retained  in  hand  as  a  margin  against  contingencies.  In  this  case 
its  value  is  104  tons,  representing  3  inches  of  draught. 

*  See  Table  of  Constants,  and  chapter  on  Resistance. 


Relation   of  Coefficients   to   One   Another     4  i 


Relation  of  the  Coefficients  to  One  Another. 

it 
Relation  coefficient,       e  =  .9,  constant  =  — • 

a 

Block  coefficient.  5  =  a./3.e. 

Area  of  water  line  coefficient, 

o ,  or         • 

e  p.e 

M id.  area  coefficient,     £  =  -,  or  — 

p         a.e 

2 

Prismatic  coefficient,     n  =  —  • 
Bilge  diagonal  coefficient, 

"  =  £t0  |j  0>  =  •«  to  .82). 


Tvri:  <»r  Vkssel. 

e 

.0 

6 

a 

0 

P 

b 

Steam  pinnaces,  30  ft.  to       \ 

.36 

.666 

.600 

.600 

.652 

60  ft f 

.9 

.36 

.666 

.616 

.600 

.652 

r 

.9 

.38 

.666 

.633 

.600 

.652 

.!) 

.39 

.666 

.649 

.600 

.652 

Steam  yachts,  100  ft.  to 

.1) 

.40 

.666 

.666 

.600 

.652 

300  ft . .  also  destroyers  « 

.0 

.41 

.670  • 

.680 

.603 

.653 

and  torpedo  craft  .     . 

.9 

.42 

.671 

.695 

.004 

.653 

.9 

.43 

.671 

.712 

.604 

.653 

.9 

.45 

.675 

.740 

.608 

.654 

.9 

.40 

.674 

.758 

.607 

.654 

.9 

.47 

.674 

.774 

.607 

.654 

.9 

.48 

.675 

.790 

.608 

.055 

Small     river     propeller 

.9 

.49 

.'•.76 

.804 

.609 

.650 

steamers,  50  ft.  to  150 

.9 

.50 

.677 

.8i'0 

.610 

.657 

ft 

r 

.9 

.51 

.679 

.834 

.611 

.059 

.9 

.52 

.680 

.849 

.612 

.661 

.9 

.53 

.683 

.800 

.015 

.603 

.9 

.54 

.688 

.S7o 

.620 

.665 

< 

.9 

.55 

.694 

.880 

.625 

.670 

Sound  and  river  steamer, 

.9 

.50 

.Too 

.890 

.630 

.676 

150  ft.  to  400  ft.     .     . 

.9 

.67 

.70:; 

.900 

.633 

.679 

.9 

.58 

.707 

.910 

.637 

.0,83 

.9 

.59 

.712 

.920 

.641 

.687 

.9 

.60 

.710 

.930 

.645 

.092 

48 


The   Naval   Constructor 


Type  of  Vessel. 

e 

.9 

5 

.58 

a 

(3 

P 

b 

c 

.677 

.950 

.610 

.657 

High      speed      channel 
steamers,    200    ft.    to 

.9 
.9 

.59 
.60 

.689 
.697 

.953 
.956 

.620 
.627 

.665 
.673 

300  ft 

.9 

.61 

.707 

.959 

.636 

.681 

f  - 

.9 

.62 

.716 

.962 

.644 

.690 

.9 

.63 

.725 

.965 

.652 

.698 

Ocean  liners,  400  ft.  to  * 
750  ft 

.9 

.64 

.734 

.968 

.661 

.706 

•~  ^ 

.9 

.60 

.743 

.971 

.669 

.714 

.9 

.66 

.755 

.975 

.680 

.722 

r  r 

.9 

.70 

.820 

.950 

.737 

.768 

i 
i 

.9 

.71 

.828 

.952 

.745 

.770 

Full-rigged  ships,  250  ft.  \ 

.9 

.72 

.838 

.954 

.754 

.777 

to  350  ft 

.9 

.73 

.847 

.957 

.762 

.785 

L 

.9 

.74 

.857 

.959 

.771 

.792 

.9 

.75 

.866 

.962 

.779 

.800 

< 

.9 

.76 

.874 

.965 

.787 

.807 

.9 

.77 

.884 

.967 

.796 

.814 

Intermediate  liners  and 
freighters,  300    ft.  to 
700  ft 

• 

.9 
.9 
.9 

.78 
.79 
.80 

.894 
.903 
.913 

.969 
.971 
.973 

.805 
.813 

.822 

.819 
.825 
.830 

.9 

.81 

.922 

.976 

.830 

.836 

.9 

.82 

.933 

.978 

.840 

.843 

I 

.9 

1 

.83 

.941 

.980 

.847 

.850 

Coefficients  of   Centers  of  Gravity  for  Various  Vessels. 

Value 
of  "g." 
Small  steamers,  as  harbor  tenders,  revenue 

steamers,  etc 65  to  .70 

Torpedo  boats .67 

Torpedo  boat  destroyers 55  to  .60 

Auxiliary  steam  yachts 65 

Full-power  steam  yachts 70 

Full-rigged  sailing  ships 69  to.  71 

Shelter-deck  intermediate  liners 60  to  .65 

Swift  ocean  liners .     .     .56  to.  58 

Shelter-deck  freighters 56  to  .58 

Three-deck  freighters,   with   poop,  bridge, 
and  forecastle      .     ,     .     .     .     .     .     .     ,     .  54  to  .  56 


Inertia   Coefficients 


49 


Moment  of  Inertia  of  Water  Line  Coefficients. 

L  x  7>'3  x  i=  I. 


W  v  obb  i.im' 

Inkkti  V 

W  LTBB  Link 

IXEKTIA 

( lOEFFICIENT, 

CoKFFIc  IFXT, 

Coefficient, 

C'OFFFlc  IKS  1  . 

"a." 

"  t." 

"a." 

II  jii 

.50 

.02250 

_  - 

.  I  •> 

.01841 

.51 

.H2310 

.70 

.04900 

.02383 

.  i  i 

.05100 

.53 

.024"  Hi 

.78 

.05233 

.54 

.02540 

.79 

.05383 

.55 

.02633 

.80 

.05500 

.56 

.02710 

.81 

.05050 

.57 

.02800 

.82 

.05783 

.58 

.02910 

.83 

.05930 

.59 

.03000 

.84 

.00075 

.60 

.03100 

.85 

.00200 

.61 

.03200 

.80 

.06341 

.02 

.03300 

.87 

.06500 

.63 

.034IHI 

.88 

.06625 

.04 

.035<  in 

.89 

.06766 

M 

.03600 

.90 

.06900 

.60 

.03733 

.91 

.07050 

.67 

.03844 

.92 

.07200 

.08 

.03955 

.93 

.07341 

.09 

.04100 

.94 

.07500 

.70 

.04200 

.95 

.07600 

.71 

.04325 

.96 

.07833 

.72 

.04500 

.97 

.07900 

.73 

.04000 

.98 

.08050 

.74 

.04700 

. 

- 

All  the  elements  insuring  the  qualities  that  embody  a  well- 
shaped  boat  of  the  particular  type  contemplated  and  at  the  same 
time  a  stable  ship  having  been  thus  determined,  the  lines  may  be 
commenced  with  the  certainty  that  no  unnecessary  alterations  will 
bt  required. 

The  freeboard  will  be  calculated  from  the  legal  tables  given  and 
explained  herein,  but  in  any  case  the  limiting  draught  consistent 
with  the  block  coefficient  determined  on  as  the  maximum  avail- 
able for  the  required  speed  should  be  taken  advantage  of. 

After  carefully  drawing  the  center  and  other  construction  lines, 
and  marking  off  the  ten  or  twenty  ordinates  that  it  is  proposed  to 


50  The   Naval   Constructor 


use,  it  will  be  well  to  have  a  definite  routine  or  method  in  which 
to  draw  down  the  various  views  comprising  what  are  embraced 
under  the  general  term  "  lines." 

To  this  end  the  following  will  prove  a  good  sequence : 

1.  The  "  dead  flat"  section  on  body  view. 

2.  Rail  sheer  line. 

3.  Contour  of  stem  and  stern  in  profile. 

4.  Rail  half-breadth. 

5.  Load  water  line  half-breadth. 

6.  Bilge  diagonal. 

7.  Transfer  L.W.L.  and  B.D.  i-breadths  to  body  plan. 

8.  Draw  freehand  the  sections  to  foregoing. 

9.  Trial  displacement  by  planimeter. 

10.    Sheer  heights  from  profile  to  body  plan. 

Taking  this  routine  in  order  :  — 

1st.  The  dead  flat  or  midship  section  should  present  no  difficul- 
ties, as  the  area  of  this  section  is  pre-determined  from  the  co- 
efficient /3.  This  being  so,  the  height  of  rise  of  floor  construction 
line  is  assigned  by  giving  the  easiest  bilge  consistent  with  the 
area  of  section  demanded.  In  no  case  should  the  bilge  be 
"squarer"  than  the  demands  of  this  area  require,  as  in  full 
vessels  sufficient  difficulty  is  encountered  in  setting  the  bilge  strake 
plates  and  bending  the  frames  without  adding  further  to  it. 

2d.  In  most  vessels,  except  yachts  and  launches,  it  will  be 
found  advisable  to  make  the  lowest  part  of  sheer  at  the  half-length 
amidships,  as  otherwise  correction  would  have  to  be  made  for 
freeboard  and  the  classification  societies'  numerals.  It  is  best, 
then,  after  fixing  the  height  of  bulwark  or  sheer  strake  above 
upper  deck  to  underside  of  moulding,  to  run  a  pencil  line  parallel 
to  L.W.L.  from  A. P.  to  F.P.,  at  which  points  and  above  this  line 
the  sheer  forward  and  aft  should  be  set  up.  The  amount  of  sheer 
will  of  course  depend  on  the  type  of  vessel,  i.e.  whether  intended 
for  sea  or  river.  In  the  latter  case  it  is  evident  the  same  amount 
of  u  spring  "  would  not  be  required  as  for  over-sea  voyages.  The 
standard  sheer  prescribed  by  the  British  freeboard  tables  will  be, 
however,  a  good  guide,  and  where  this  is  deemed  insufficient  or 
where  special  cases  suggest  a  departure  from  these,  as  in  passenger 
steamers  and  first  class  ocean  liners,  a  handy  rule  and  one  that  gives 
a  very  symmetrical  sheer  is  to  take  one-fifth  of  the  vessel's  length 
in  feet,  calling  the  quotient  inches  which  will  equal  the  amount 
of  sheer  forward.     One-third  of  this  will  be  the  sheer  aft,  as  :  — 

Length  in  feet      „,         „  .  .     .     , 

= — - —       -  =  Sheer  forward  m  inches, 

o 

,                 Sheer  forward      _,,  „    .     .     , 

and, =  Sheer  aft  in  inches. 


Inertia   Coefficients  51 

The  amount  of  sheer  having  been  decided  upon  with  the  lowest 
part,  Bay,  at  the  half-length,  the  quickest  and  simplest  way  to  run 
the  sheer  line,  insuring  a  fair  curve,  will  be  to  divide  the  hall- 
length  before  and  abaft  the  lowest  sheer,  into  four  equal  parts, 
and  at  each  of  these  points  set  up  the  perpendicular  heights 
obtained,  as  under,  postulating  in  this  case  that  the  sheer  at  F.P. 
is  equal  to  82  inches,  and  the  sheer  at  A.P.  :)0  inches,  giving  a 
mean  sheer  of  50  inches,  as  per  freeboard  table-. 

82"  x  1.000    =  82"  sheer  at  4th  station  =  F.P. 
82"  x    .662    =  46"  sheer  at  3rd  station  forward  of  lowest 
82"  X    .250    =  20r'  sheer  at  2d  station  forward  of     " 
82"  X    .0625  =    5>"  sheer  at  1st  station  forward  of     " 

and  for  the  sheer  aft :  — 

30"  x  1.000   =  30"  sheer  at  4th  station  =  A. P. 
30"  X    .502    =10 '"sheer  at  3d  station  abaft  lowest 
30"  X    .250   =    7|"  sheer  at  2d  station  abaft      " 
30"  X    .0625  =    If"  sheer  at  1st  station  abaft      " 

By  pinning  the  spline  to  these  spots  and  adjusting  the  free  ends 
to  the  eye,  an  absolutely  fair  sheer  line  may  be  run  in,  bearing  in 
mind,  however,  that  in  ships  with  a  very  full  rail  line  forward. 
compensation  must  be  given  on  the  sheer  to  adjust  the  great  dis- 
parity in  the  length  of  the  half-breadth  rail  line  and  the  same  line 
projected  on  sheer  plan;  as,  if  this  be  not  done,  the  rail  line  on  model, 
and  of  course  on  the  actual  ship,  will  appear  as  -'rounding  down." 

3d.  The  contour  line  of  the  stem  will  be  very  much  a  matter 
of  individual  taste,  although  above  water  line  it  is  usual  to  make 
it  straight  unless  in  special  cases.  By  "straight"  is  meant 
"apparently"  so,  as  it  is  customary  to  give  about  f-inch  round 
on  face  of  stem  from  where  it  leaves  the  top  of  the  forefoot  curve 
to  stem  head,  an  absolutely  straight  line  adjoining  a  curve  appear- 
ing as  slightly  hollow.  Also,  it  is  not  advisable  to  make  the  stem 
plumb,  as  the  illusion  in  that  case  is  to  make  it  appear  as  leaning 
aft.  A  rake  forward  of  about  twice  the  moulding  of  the  stem 
head  is  common.  In  outlining  the  stern  and  counter  the  same 
remarks  as  to  taste  apply,  care  being  taken  that  the  counter  line 
where  it  meets  the  rudder  post  is  carried  by  an  imaginary  curve 
to  harmoniously  meet  the  arch  of  body  post.  The  counter  line, 
from  knuckle  moulding  to  stern  post,  should  be  perfectly  straight 
—  not  hollow.  A  hollow  to  this  line  gives  the  appearance  of  "an 
overweighted  overhang,  and  a  brokensheer,  besides  making  the 
plating  more  difficult  to  sit. 


52 


The   Naval   Constructor 


Dimensions  of  Figureheads  and  Lacing  Pieces. 


Fig.  12. 


A 
Length  of 

B 

Size 

C 
Depth  of 

D 

Length  of 

Figure 

Outside  of 

Stem. 

Vessel, 
B.S. 

of  Lacing 
Piece. 

Figure- 
head. 

Feet. 

Inches. 

Inches. 

Feet.  Inches. 

450 

12f 

30i 

9        6 

400 

12 

28i 

9        0 

350 

Hi 

26| 

8         0 

300 

101 

25 

8         0 

250 

9| 

23£ 

7         G 

200 

9 

211 

7         0 

150 

H 

19| 

6         6 

100 

n 

18 

6         0 

N< 

)TE.  —  Angle  o 

f  lacing  piece, 

45°. 

The  length  of  overhang  of  course  cannot  be  arbitrarily  fixed, 
but  a  very  fair  proportion  for  ordinary  freighters  is  J¥  to  ■£%  of  the 
length.  The  height  of  deck  or  rail  at  taffrail,  or  "  cock-up,"  will 
be  dependent  on  the  camber  of  deck  at  transom  frame  (No.  0). 
The  midship  camber  proportioned  to  the  half-breadth  at  this 
frame  should  be  set  up  and  the  deck  line  carried  through  this 
spot  in  a  fair  curve  to  taffrail.  The  height  so  obtained  should  be 
then  transferred  to  body  plan,  and  the  deck  (or  rail  line)  between 
No.  0  section  and  taffrail  drawn  in  as  a  round  of  beam  curve,  from 


Fi 


lyurcn 


cads 


53 


which  may  be  obtained  the  intermediate  spots  for  deck  at  side  (or 
rail)  on  sheer  plan. 

4th.  The  rail  half-breadth  will  depend  on  the  particular  type 
of  ship  being  designed.  In  freighters  it  will  be  parallel  to  the 
center  line  for  probably  half  the  length  amidships,  whereas  in 
yachts  and  other  tine  vessels  it  will  "round  "  all  the  way.  It  is 
convenient  to  have  rail  half-breadths  at  hand  for  various  types  of 
vessels  for,  say,  ten  ordinates  with  half-end  ordinates  or  which- 
ever number  is  adopted  as  the  standard.  These  should  be  tabu- 
lated with  the  half-breadth  amidships  as  unity,  when,  with  the  aid 
of  a  slide  rule,  the  half-breadths  for  the  design  may  be  very  rapidly 
proportioned.  It  will  be  found  convenient  to  have  these  for 
liners,  freighters,  sound  and  river  steamers,  yachts,  etc.,  from 
good  examples  of  their  respective  classes.  The  contour  of  rail  line 
around  taffrail  will  require  careful  fairing  into  the  A. P.  ordinate 
spot,  and  also  at  center  line,  where  in  no  case  should  it  be  per- 
fectly straight,  the  effect  of  such  being  a  hollow.  Neither,  on  the 
other  hand,  should  it  come  to  a  "peak"  or  point,  but  carefully 
drawn  as  an  arc  of  a  circle.  The  knuckle  mouldings,  whether 
they  be  one  or  more,  may  with  advantage  be  delineated  by  tracing 
the  rail  line  just  drawn  and  transferring  it  forward  to  its  exact 
location.  By  so  doing  it  will  be  seen  that  the  stern  between 
knuckle  and  rail  lines  will  develop  with  a  pleasing  gradation  from 
'•  O  "  frame  to  the  upper  counter  line. 

Table  of  Rail  Half-Breadths  for  Various  Types. 


Ordi- 
nate*. 
'0"=A.P 


0 
i 
1 

9 


0 

I 

8 
0 

9\ 
1" 


OCEAN" 
LlNEK. 


.ono 

.714 
.786 
.882 
.946 
.985 
1.000 
.989 
.834 
.820 

.358 

Stem 


H  r. 

H    ~ 


.444 

.757 

.889 

.990 

l.Oi  io 

1.000 

1.000 

1.000 

1.000 

.985 

.850 

.572 

Stem 


7-    Z- 


.756 
.812 
.854 
.918 
.951 
.988 
1.000 
.991 
.005 
.801 
.727 
.676 
.355 


X 

ob 

**» 

£  a 

Sail- 

.". — 

>; 

ing 

■-~s. 

«B 

Ships. 

02 

J 

Oce- 
anic. 


.756 

.603 

.603 

.829 

.730 

.691 

.872 

.810 

.772 

.934 

.910 

.875 

.077 

.907 

.955 

.994 

.979 

.995 

1.000 

1.000 

1.000 

.994 

.979 

.978 

.90:, 

.960 

.930 

.877 

.910 

.803 

.619 

.740 

.532 

.300 

.615 

.298 

Stem 

Stem 

Stem 

.655 
.790 
.845 
.912 


.987 
1.000 
.971 
.044 
.884 
.606 
.404 
Stem 


54 


The   Naval   Constructor 


5th.  The  load  water  line,  as  already  stated,  must  circumscribe 
the  area  calculated  with  the  aid  of  the  coefficient  a.  The  method 
of  obtaining  a  has  been  previously  explained.  To  obtain  the  form 
of  this  water  line,  and  at  the  same  time  insure  the  accuracy  of  the 
required  enclosed  area,  it  will  be  found  advantageous  to  prepare  a 
diagram  similar  to  the  one  opposite,  or  this  one  may  be  used  with 
the  aid  of  proportional  compasses.  Opposite  the  value  of  a  for 
the  design  in  hand  half- breadths  for  ten  ordinates  may  be  read  off 
and  transferred  to  the  half-breadth  plan.  Should,  however,  the 
line  delineated  after  the  spline  has  been  fixed  not  meet  with  the 
designer's  individual  taste,  or  where  greater  fullness  or  fineness  is 
required  for  special  cases,  forward  or  aft,  it  will  be  a  very  simple 
matter  to  modify  the  line,  at  the  same  time  observing  that  what- 
ever area  be  cut  off  at  any  one  point  be  compensated  for  elsewhere 
on  the  water  line,  as  the  offsets  taken  from  the  diagram  will  en- 
close exactly  the  area  required.  Of  course  the  designer  may  make 
his  own  diagram  for  the  number  of  ordinates  he  prefers  to  design 
with.  In  any  case  the  run  of  the  line  for  a  few  feet  forward  of  the 
post  will  require  special  adjusting  when  the  oxter  is  being  faired. 

In  addition  to  the  diagram,  the  following  table  is  given  of  actual 
load  water  lines  of  several  types  with  the  coefficients  of  area  of 
same  (a). 

Load  Line  Half-Breadths  Standardized. 


Ordi- 
nates. 

Fast 
Ocean 
Liner. 

H 
h 
W 

O 

H 

s.s. 

Yacht. 

A3 

M 

>  H 

Sail- 
ing 
Ship. 

w 

<< 

H 

cg 

Oce- 
anic. 

"0"=A.P. 

a  =.72G. 

a  —.857. 

a  =  .683. 

a  —.717. 

a  =.797. 

a  =.65G. 

a  =.771. 

0 

Post 

Post 

Post 

Post 

Post 

Post 

Post 

l 

.289 

.448 

.148 

.382 

.407 

.275 

qqq 

1 

.531 

.770 

.479 

.642 

.678 

.483 

.631 

2 

.828 

.980 

.818 

.884 

.898 

.750 

.892 

3 

.945 

1.000 

.948 

.977 

.965 

.900 

.977 

4 

.988 

1.000 

.909 

1.000 

.992 

.980 

.995 

5  = 

1.000 

1.000 

1.000 

.987 

1.000 

1.000 

1.000 

6 

.976 

1.000 

.928 

.932 

.989 

.900 

.980 

7 

.881 

1.000 

.793 

.791 

.955 

.760 

.942 

8 

.670 

.985 

.578 

.578 

.830 

.550 

.775 

9 

.357 

.781 

.328 

.308 

.537 

.303 

.440 

H 

.180 

.464 

.150 

.154 

.282 

.182 

.228 

10 

Stem 

Stem 

Stem 

Stem 

Stem 

Stem 

Stem 

L.W.L.    Half-Breadths 


55 


Cth.  The  construction  line  for  the  bilge  diagonal  is  variously 
drawn  from  rise  line  or  base  line  ;  but  the  latter  is  the  more  use- 
ful, being  adaptable  to  extremes  of  types  and  unaffected  by  rise 
of  floor  line  ;   i.e.,  the  line  should  be  drawn  diagonally  across  the 


.G<j 


DIAGRAM  OF  BILGE  DIAGONAL  OFFSETS 

"b" 


FOR  VARIOUS  VALUES  OF 
(TEN  ORDINATES) 


<f> 


=' 

J- 

^ 

1    JJM" — 

n 

^ 

^tTi      L 

^-T 

'  12 

■^1 

,-"' 

^_,  9-^ 

y 

/T 

_ — — "        ,^ 

j?~~* 

2    *- 

^ 

^ 

• 

/          \       \    y 

8J^ 

^ 

V^ 

/ 

/ 

/ 

^^ 

9^/ 

___^—p^^^ 

/ 

'l 

' 

i  / 

^^ 

I  J^| 

/ 

Ivr 

n 

Ml 

4H 

. 
^y^ 

^< 

^ 

UH"" 

' 

I 

-^-^    " 

ijjq 

^_^---^*^**'^ 

-""■""'^ 

•- 

C.L  C 

F  SHI 

P 

.7  .75  .8  .85 

VALUES   OF'V  ^COEFF.OFB.D.) 
Fig.  13. 


10 


9' 


.y 


body  plan  from  the  intersection  of  the  base  with  tlie  half  moulded 
breadth  line  to  center  line  at  load  water  line  height.  It  is  evi- 
dent that  the  area  enclosed  by  this  line  must  bear  a  close  relation- 


5G 


The  Naval   Constructor 


ship  to  the  prismatic  coefficient  which  varies  with  p  and  is  equal 

to  —  to  ■—  where  p  ranges  from  .CO  to  .82,  respectively. 

By  determining  the  value  of  the  bilge  diagonal  coefficient  "6," 
and  referring  to  the  diagram  opposite,  the  offsets  for  a  line  enclos- 
ing an  equivalent  area  may  be  taken  off  and  run  as  a  half-breadth 
line. 

DIAGRAM    OF    L.  W.  L.    HALF-BREADTHS 
FOR   VARIOUS    VALUES   OF    "a" 
(TEN    ORDINATES) 
5    OR  <!>  5 


w 

z 
o 

H 
ir 
O 
a. 
o 
<r 
a. 

x 

H 
D 
< 
u 
cc 

CD 


X 


0' 

_4_ 

G 

40' 

-9/ 

9 

3 

7, 

J*- 

n' 

b' 

— 

8, 

-7' 

7 

p--^ 

0 

• 

-6' 

b' 

9 

-5' 

5 

■4.' 

4 

J 

•J£ 

1, 

-3' 

3 

-2/ 

2 

'-< 

-1' 

1 

D.I 

.0 

'■  s 

HI 

P 

— 

.6 


.65 


.7 


.75 


.8 


.85 


values  of"0c"  (coeff.  of  l.w.l.) 
Fig.  14. 

7th.  The  load  water  line  and  bilge  diagonal  half-breadths  hav- 
ing been  preliminarily  faired,  may  be  lifted  off  on  a  slip  of  pa- 
per and  transferred  to  body  plan  construction  lines,  when  there 
should  be  no  difficulty  in  drawing  in  freehand  the  sections,  having 
the  "dead  flat"  section  as  one  extreme  guiding  curve  and  the 
transom  frame  as  the  other. 

8th.    After  the  preceding  sections  have  been  carefully  outlined 


Bodv    Flan   ol   "Oceanic" 


57 


BODY  PLAN  OF  "OCEANIC" 


LENGTH  B.  P.   685'-3i",   B.MLD.   68'-2*,   D.  MLD.  49'-l\ 
SECTIONS  63.  537'  APT. 


STATION 


... 

STATION  No.    ' 


s  No.  H 


STATir  •. 


fcTATIQN  NQ, 
STATION  No.  i 


32  FT.    W.  L. 


ELEMENT  COEFFICIENTS 

AREA  OF  MID.    SECT.      3  =    .898 

BLOCK  CO-EFF.  A  =    .fiee 

PRISMATIC  CO-EFF.  .   _p  =    .742 

AREA  OF  L.  W.  L.  (I  =    .  771 

BILGE  DIAGONAL b  =    .723 

RELATION  CO-EFF.  £  =    .985 

Fig.  15. 

to  eye  with  the  guide  spots  mentioned,  the  planimeter  should  bo 
used  to  take  a  trial  displacement,  on  the  result  of  which  will  de- 
pend how  near  the  designer's  judgment  has  determined  the  true 
section  line.  In  any  case  he  cannot  have  got  far  away,  and  a  very 
slight  alteration  (if  any)  is  all  that  will  be  r»  quired. 

Orh.    The   sheer   heights    may  now  be  taken  from    profile  and 
spotted  on  body  plan,   level  lines  being  struck   across  at   these 


58 


The   Naval   Constructor 


heights  on  which  to  set  off  the  rail  half-breadths  previously  run  in 
plan,  as  described  in  paragraph  4.  This  will  enable  the  completed 
body  plan  to  be  drawn  in  approximately,  from  which  spots  may 
be  obtained  to  fair  up. 

Having  got  thus  far,  the  final  work  of  fairing  will  be  a  compara- 
tively easy  matter.  A  buttock  line  half-way  out  on  the  counter 
will  prove  a  very  useful  line  for  this  purpose,  thereafter  taking 
buttock  and  water  line  alternately  until  the  whole  body  is  faired. 
Where  great  fairness  is  required,  a  complete  set  of  diagonal  lines 
should  be  run  ;  but  ordinarily  this  is  unnecessary,  unless  in  small 
craft  where  the  sections  are  intended  directly  for  the  floor  with- 
out further  fairing. 

The  following  will  prove  a  suitable  method  for  designing  and 
fairing  the  bossed  plaiting  enclosing  after-end  of  shafting.  Hav- 
ing determined  the  outside  diameter  of  the  boss  of  spectacle  frame, 
lay  off  the  distance  to  outer  edge  of  boss  barrel  at  forward  end  of 
same  on  the  half-breadth  plan,  as  at  A.  Then  take  another  spot 
at  the  fore  end  of  the  stern  tube  equal  to  the  siding  of  the  vessel's 
bulkhead  frame  plus  one  inch  clear  of  the  stuffing  box  flange  on 
the  stern  tube  bulkhead  at  "  (7."  Through  these  two  spots  con- 
tinue a  straight  line  until  it  intersects  the  water  plane  at  the  shaft 
center  level  "D."     The  angular  space  formed  by  the  junction  of 


Bhc! 


Fig.  16. 


the  water  plane  mentioned  and  the  projected  line  should  then  be 
carefully  faired  into  the  eye  with  a  spline,  when  the  resulting  line 
will  give  you  half-breadths  at  the  shaft  center  height.  These  half- 
breadths  being  transferred  to  the  body  plan,  radii  should  be  struck 
through  them  giving  the  contour  of  the  bossing,  which  may  be 
continued  freehand  into  the  frame  sections  above  and  below  the 
boss,  observing  that  the  general  tone  harmonizes  with  the  outline 
of  spectacle  frame  previously  drawn  in,  in  accordance  with  the 
form  advocated  under  that  heading. 

Having  outlined  the  form  of  bossing  on  body  plan,  three  diago- 
nal lines  should  be  struck,  the  lower  one  intersecting  the  arcs 
forming  oxter  under  spectacle  frame,  the  middle  one  through  the 


B 


OSSlIli 


59 


center  of  shaft,  as  shown  to  diagonal  1|,  and  the  other  making  a 
like  intersection  with  the  curves  of  the  slope,  as  shown  on  the 
diagram.     These  diagonals  may  now  be  lifted  off  and  run  in  the 

DIAGRAM 

SHOWING 
METHOD  OF  DESIGNING  BOSSING, 


Fig.  17. 


usual  way  on  half-breadth,  faired  up,  and  retransferred  to  body 
plan,  thus  permitting  of  same  being  more  accurately  delineated, 
as  it  will  be  remembered  these  were  originally  drawn  freehand. 


60 


The   Naval   Constructor 


Elements  of 


Piston 

Speed. 

Class  of  Steamer. 

r       I-1 

0  3  t- 

'A  H 

ago 

Ft.  per 
Min. 

Type  of 
Propeller. 

Type  of 
Engine. 

400 

500 
600 

700 
700 

Paddle. 
River  paddle  steamer    .... 

River  paddle  steamer    .... 
River  paddle  steamer    .... 

River  paddle  steamer    .... 

(  Sea    paddle   steamer,  heavier  ) 
\     paddle  wheels  required  .    .    j 

13-15 

15-17 

18-22 

18-22 
18-22 

\  Side  wheels 
(   feathering 

U             11 

(i         it 
i<         it 

Inclined 
u 
(i 

si 

530 
530 

600 
600 

Cargo. 
Ordinary  freight,  300  to  450  .     . 
Ordinary  freight,  300  to  450  .     . 
Ordinary  freight,  300  to  450  .     . 
Ordinary  freight,  300  to  450  .     . 

4-11 
11-13 
11-13 
11-13 

Single  screw 
Twin  screw 

(I            u 

Inverted 

a 
(i 
t< 

700 
750 

Cargo  and  Passenger. 
Intermediate  steamships,  450-600 
|  Very  large  intermediate,  cargo  I 
(  and  passenger,  600  and  over  .    ) 

13-16 
14-16 

Single  screw 
Twin  screw 

Inverted 

it 

800 
800 
950 
950 
950 

Ocean  Liners. 
Passengers  and  mail     .... 
Passengers  and  mail      .... 
Passengers  and  mail      .... 
Passengers  and  mail      .... 
Passengers  and  mail     .... 

16-19 
16-19 
19-23 
19-23 
19-23 

Single  screw 

Twin  screw 
K        it 

u             (< 

U                 (1 

Inverted 

(i 

(i 
c< 

it 

800-910 

Fast  channel  &  sound  steamers 

19-23 

Twin  screw 

Inverted 

950 
950 
950 

Battleships  &  cruisers,  1st  class 
Battleships  &  cruisers,  1st  class 
Battleships  &  cruisers,  1st  class 

23 
23 
23 

Twin  screw 

u           « 
(1            11 

Inverted 

1,200 

(  Torpedo-boat    destroyers    and  ) 

30 

Twin  screw 

Inverted 

5,700 
6,000 
6,200 
7,000 
10,000 

8,000 

Turbine-driven   Vessels. 
(  Turbine  river  steamer  and  tur- ) 
I      bine  steam  yachts  .    .     .    .    f 
(  Turbine-driven  Atlantic  liner,  j 
|     passenger  and  mail     .     .     .    i 
(  Turbine-driven  pass,  and  mail  ) 
\     channel  and  sound  steamers  ( 
i  Turbine-driven    torpedo  -  boat  ) 
\     destroyer  and  scout    .     .     .    f 
(  Turbine-driven    torpedo  -  boat  | 
|      destroyer  and  scout    ...    1 
(Small  44-ton  displacement  ex- ) 
J     perimental  vessel,  low  coal' 

16-22 

22 
25 
30 
36 

32 

f  Multiple 
\     screw 

[I               u 
a           1 1 
(i            (< 

U                 (1 
U                  II 

Hor. 
Comp. 

[(          u 

U            (t 

((        11 

11        i( 

Hor. 
Triple 

*  By  permission  of 


Engine   Room    Lengths,  etc. 

Marine  Engines.- 


61 


MA<   II1NKKY    PARTM   I  I.AKS. 

|fl  L 

Number  of 

Cylinders 
iii  Each 

Engine. 

Cylinder 
Ratios. 

Type 

of 

Boilers. 

Boiler 

Press. 
Lbs. 

Boiler 

Draft. 

«-l  o 

2-Conip. 
Side  by  sid.' 

1  to  3.5 

Cyl, 

1<>0 

Nat. 

6.50 

it      n 

ii     it 

ii 

110 

Forced 

. 

7  22 

(i      (i 

ii     ii 

LOCO. 

120 

ii 

11.00 

3-Triple 
Side  by  side 

1  :  2.16  :  4.82 

Cyl. 

160 

1 1 

•    • 

10.00 

(i      it 

it                   ||                   l| 

« 

II 

tt 

•    • 

9.00 

3-Triple 

1  :  2.65  :  7.1 

Cyl. 

175 

Nat. 

4.85 

(i      it 

ii        .. 

tt 

200 

Forced 

,         , 

6.00 

it      it 

ii        K        ii 

ii 

tt 

tt 

,         , 

5.85 

4-Quad. 

1  :  '-'.1  :45:  9.14 

.     .     . 

214 

it 

•    • 

5.45 

3-Triple 

1  :  2.65  :  7.1 

cyl. 

200 

Nat. 

5.12 

4-Quad. 

1  :  2.07  :  4.24  :  8.82 

it 

■_'14 

A  ssist. 

•    • 

4.37 

3or4-Triple 

1  :  2.6-5  :  6.38 

Cyl. 

180 

Nat. 

7.00 

h       ii 

II                 II                 tt 

II 

it 

Forced 

6.00 

4-Triple 

1  :  2  07  :  6.37 

II 

ii 

Nat. 

6.16 

6-Qu;td. 

1  :  2.08  :  4.16  :  8.71 

. . 

220 

tt 

5.95 

6-8  Qua. 1. 

(i        «<         ii 

II 

CI 

Forced 

•     • 

6.25 

4-Triple 

1  :  2.28  :  5.84 

Cyl. 

180 

Forced 

•     ■ 

8.00- 
9.70 

4-Triple 

1  :  2.26  :  7.00 

Cyl. 

175 

Nat. 

8.50 

ti      i< 

ii        tt        ii 

it 

ii 

Forced 

10.00 

>i      ii 

ii        ii         it 

W.  Tube 

250 

Nat. 

•    • 

12.00 

4-Triple 

1  :  2.36  :  5.50 

Yarrow 
W.  Tube 

250 

Forced 

•    • 

41.00 

\"  Expansions. 

Parson's  i 
Tnrbine  | 

126 

Cyl. 

150 

Forced 

Super- 

12.00 

1?.-, 

W.Tube 

180 

it 

lu  -ated 
steam 

16.00 

X             II 

1 25 

it 

170 

ti 

•     • 

20.00 

It 

ii 

.. 

• 

55.00 

. .           It 

.. 

it 

• 

70.00 

11 

•      150 

it 

150 

•• 

•     • 

100.00 

J.  'alder,  B.Sc. 


62  The  Naval  Constructor 


Level  lines  as  shown  at  l2,  h,  h,  etc.,  are  now  drawn  from  the 
point  of  intersection  of  frame  with  diagonals  1  and  2,  and  the 
half -breadths  taken  off  at  these  levels  and  finally  faired-up  on 
half-breadth,  when  it  will  be  found  that  the  resulting  horizontal 
ribband  line,  besides  acting  as  a  check  on  the  fairness  of  the  di- 
agonals, will  show  the  "  wind  "  of  the  shell  plating  wrapping  into 
oxter  and  body  post  and  insuring  a  natural  "  snye  "  without  any 
chance  of  "  gather  "  or  unfairness. 

The  oxter  underneath  the  ship's  counter  may  be  faired  in  a 
similar  manner. 


Engine   Room    Lengths 


»;:; 


Engine  Room  Lengths. 


r  fc  ~ 


'•  ??  .* 
^  *  - 


E/6" 

10  6 
12  0 

12  3 

13  6 

14  0 
16  0 

16  6 

17  0 

18  0 
18  4 
20  0 
20  0 
20  0 

20  0 

21  0 

21  0 

22  0 
22  0 
22  0 
22  0 


S  l  / 1 ■:  <  1 1 ' 
Engines. 


1O"&20" 

22  &  40 


27 
17  &  26 

20 

r,  &  30 

21 


11, 

17, 
11 

17 

10, 

16, 

26 

21 

o 

3  &  46 

36 

13}, 

_  _ ._. , 

36 

24 

19, 

30, 

50 

30 

18, 

28, 

45 

30 

21}, 

31,  : 

M.  34 

20 

21, 

34, 

56 

40 

18, 

27, 

42 

24 

18} 

,27, 

42 
T 

18 

21, 

34. 

59 

36 

17, 

26J, 

40 
T 

24 

24, 

40, 

63 

12 

22, 

36, 

57 

36 

19, 

32, 

52 

-  n 

-  v  - 


>  '  - 


36 


8,_62 

36 
24,   38,   62 

36 


2>/()'/ 

23  0 

24  0 
24  0 
26  0 
26  0 
26  0 
26  0 
26  0 

26  6 

27  0 
27  6 
27  6 

27  6 

28  0 
28  0 
28  0 
28  0 

28  3 


Si/,  i:  OF 
ENGIS  I  8. 


10", 31", 54" 

~  42" 

27,  40,   65 

36 

inj/28,  30,_r>7 

36 

30,  45,  70 

28,  46,  75 

18 
22,  36,  59 

42 
25,  41.1,  68 

42 
23^,39,  65 

42 
22,   35,   59 

62 

30,  50,  80 

54 

28,  46,  75 

4  s 

25,  42},  72 

4S 

31,  52,   83 

54 
25, 42},  72 

48 
28,  46,   76 

48 
29^4.-.,    74 

~  48 

32,  52,   81 

54 
30,  50,  80 

54~ 
19,28},  41,60-, 

42 
19},28f,30f,30t 

IS 


r  fe  ~ 

- 


Size  of 
Engines. 


32'  0" 

34  0 

34  0 

35  <> 

35  0 

36  0 

39  7 

40  0 
40  0 
42  0 
45  0 

47  6 

48  0 
48  0 
48  0 

59  0 

60  o 
62  6 
74  0 
77  6 


2 1.'",  :\a:.",  aw.",  7o' 

36" 

32£,  59,  92 


T. 


42 
24,  34,  48,  68 

42 
32},  59,  !»2 

54 
40,  66,  106 

72 

32,  52,  60,  60 

42 
29,  46,  72 

48 
31,43,60,86 

54™ 
33},  51,  78 

48 
34|,  53,  63,  63 

48 
30,  43,  63,  89 

60 
32,  45},  66,  66,  66 

54 

35,  50,  70,  100 

66" 
28},  28},  55,  77,  77,  77 

i;o 
43,   69,  79 

60 

40},  55,  7 1 ,  77,  77 

r,o 
40},  55,  77,  77,  77 

54 

,  50},  7:;;.  Jn-, 

69 

49},  73,  95,  95,  95 

60 


T. 

T. 

'J-. 
T. 


37,  37,  79,  98,  98 , 

"~ 69 


Twin  Beta  aoted  with  ••  T." 


64 


The   Naval   Constructor 


CHAPTER  III. 
THE  PREPARATION  OF  SPECIFICATIONS. 

Too  much  care  cannot  be  expended  in  the  drafting  of  the  hull 
specification.  Clearness  and  conciseness  should  be  aimed  at 
consistent  with  an  embodiment  of  all  details  of  hull,  fittings,  and 
outfits  supposed  to  be  supplied,  and  all  repetition  or  ambiguity  of 
phraseology  carefully  avoided.  Hampering  restrictions  should 
be  left  out.  Know  your  requirements  and  state  them  distinctly. 
As  in  all  other  ship  construction  work,  it  will  pay  to  have  a 
definite  routine  or  system  in  which  to  draft  the  specification.  Of 
course,  it  is  obviously  impossible  to  have  a  standard  specification 
which  shall  apply  to  all  ships,  as  vessels  are  so  diverse  in  their 
types,  design,  construction,  and  equipment  as  to  make  this  an 
impossibility.  But  by  keeping  a  routine  list  of  headings  of 
paragraphs  before  one,  and  taking  these  in  rotation  when  drafting 
the  clauses,  the  liability  to  omit  important  requirements  is  reduced 
to  a  minimum,  besides  the  saving  in  time  and  distraction  of 
thoughts  through  having  to  recollect  what  comes  next.  For  this 
purpose  the  following  headings  have  been  selected  which  will 
apply  to  ordinary  vessels.  Of  course,  for  special  types  these  will 
require  modifications  and  additions  which  will  suggest  themselves. 

Specification  Headings. 


Title  giving  type  of  vessel. 

1.  Dimensions,         moulded 

length,  breadth  and 
depth,  depth  of  hold,  load 
draft  and  deadweight. 

2.  Classification.    The  Govern- 

ment laws  to  which  the 
vessel  and  her  equipment 
are  to  conform,  also  full 
particulars  of  the  class 
she  is  to  take  at  the 
Classification  Society 
concerned. 

3.  General  Description.      Type 

of  stem  and  stern, 
number  of  decks,  laid  or 
otherwise,      length     and 


4. 
5. 

6. 

7. 
8. 


character  of  erections, 
number  of  masts.  Num- 
ber of  passengers,  de- 
scription of  housing  of 
passengers,  officers,  and 
crew.  Nature  of  cargo 
and  handling  appliances. 
Location  of  machinery, 
and  any  special  features 
of  the  vessel. 

Material  of  hull  and  rivets. 

Keel,  and  centre  girder  in 
double  bottom  ships. 

Bilge  or  side  fenders  and 
mouldings,  docking  keels. 

Stem. 

Stern  frame. 


Specification   Headings 


GO 


9. 

10. 

11. 
12. 


13. 

14. 
15. 
1(3. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 

24. 
25. 

26. 

27. 

28. 


29. 


30. 
31. 

32. 
33. 

34. 


35. 
36. 
37. 


Shaft  brackets. 

Rudder    and     stock    (also 

trunk  and  bearing). 
Shell  plating. 
Inner     bottom,      including 

plating,       side      girders, 

floors  and  margin  plate. 
Scantling      in    machinery 

space. 
Peak  tanks. 
Deep  tanks. 
F.  W.  storage  tanks. 
Steel  decks  anil  flats. 
Transverse  bulkheads. 
Longitudinal  bulkheads. 
Bunkers,  oil  or  coal. 
Engine  and  boiler  casings. 
Shaft  tunnels. 
Oil  trunks,  expansion. 

Centre  keelson    \  Loomed 
Side  keelsons      f  ghipg 

Hold  and  'tween  deck 
stringers. 

Panting  arrangements. 

Frames  and  reverse  frames, 
in  double  bottom,  up 
sides  and  at  ends. 

Floors,  throughout  in 
single-bottomed  ships,  at 
ends  and  tail  brackets  in 
double  bottom  ships,  also 
reference  to  No.  12. 

AVeb  frames. 

Deck  beams  and  knee 
brackets. 

Stanchions  to  beams. 

Strong  beams  in  E.  and  B. 
space. 

Hatchways  and  coamings, 
in  oil  or  cargo  spaces, 
covers,  fore  and  afters, 
bearers,  etc. 

( !argO  and  coal  ports. 

Grain    trimming    hatches. 

Chain  lockers. 


38.  Machinery  Foundations; 
main,  auxiliary  and  deck 
machinery,  also  boiler 
saddles  and  shaft  and 
thrust   bearing    seats. 

Sheet  steel  bulkheads. 

Steel     deck    houses,    other 
than  erections. 

Bridges,  navigating  or  dock- 
ing. 

Steel  masts. 

Steel  kingposts. 

Steel  derricks,  spars,  etc. 

Wood      masts, 
and  spars. 

Wood  decks. 

Wood  deck  houses. 

Ceiling  and  sparring 

Boat  stowage. 


39. 
40. 

41. 

42. 

43. 
44. 
45. 

4G. 
47. 

48. 
49. 
5(>. 
51. 


kingposts 


stowage. 


Anchor 

Watertight  doors  and  scut- 
tles. 
General    description    of  joiner 
work,  including  entrances  and 
stairways: 
52.    In  passengers'  quarters. 

In  officers'  quarters. 

In  crew's  quarters. 

Pantry  accommodations. 

Galley  accommodations. 

Ice  room. 

Sidelights   and  decklights; 
also  borrowed  lights. 

Cattle  fittings. 

Hawse  pipes. 

Bollards  and  fairleads. 

Hold  ladders. 

Ladders    to    erections  and 
bridges. 

Davits,  boat  and  anchor,  also 
provision  or  coaling  day  its. 

Kails,    bulwarks,   also  rail 
and  awning  stanchions, 
running  rig- 


53. 
54. 
55. 
50. 
57. 
58. 

59. 
00. 
61. 
62. 
03. 

04. 

65. 

66. 


Standing  and 


gmg, 


including 


boom  handling  gear. 


cargo 


M 


The   Naval   Constructor 


G7.    Sails,  covers,  and  awnings. 

08.  Cement  and  tiling. 

09.  Paint  work. 

70.  Heating  system. 

71.  Lighting  system. 

72.  Ventilating. 

72a.  Refrigerating  system. 

73.  Deck  Machinery,  including 

windlass,  winches  and 
capstan,  also  steam  and 
exhaust  piping. 

74.  Fresh  and  salt  water  ser- 

vice. 

75.  Fire,  pumping  and  drain- 

ing system. 

75a.  Cargo  oil  system. 

70.  Scuppers,  from  all  exposed 
houses,  etc.,  and  from 
sanitary  quarters. 

77.  Engine  room  and  docking 

telegraphs. 
77a.  Steering  gear. 

78.  Anchors,  chains,   and  line 

outfit. 

79.  Boats  and  outfits. 

80.  Flags,  etc. 

81.  Hose,  fire  and  wash  deck, 

also  fire  buckets. 

82.  Oil  tanks,  for  lamps,  etc. 

83.  Steaming  lights. 

84.  Lamps  and  lanterns,  also 

rockets,  etc. 

85.  Navigating  instruments. 

86.  Boatswain's  stores. 

87.  Carpenter's  stores. 

88.  Cargo  handling  gear,  slings, 

hooks,  etc. 

89.  Cook's  or  galley  outfit. 

90.  Cabin  outfit. 

91.  Cutlery  outfit. 

92.  Crockery  and  glass. 

93.  Table  linen. 

94.  Bed  linen  and  bedding. 

95.  Spare  glasses  for  side-lights 

in  passenger  ships. 
90.    Galvanizing. 


97.  Trim  and  stability. 

98.  Plans  to  be  furnished  own- 

ers. 

Capacity  and  dead- 
weight. 

General  arrangement. 

Cabin  booking  plans. 

Piping  plans. 

Stability  curves  and 
information. 

99.  Docking. 

100.  Trial  trips. 

101.  Inspection      fees     Cclass, 

etc). 

102.  General  clause  relating  to 

material,  workmanship, 
inspection  by  owners, 
alterations,  extras,  etc. 


Flags. 

National  colors. 
House  flags,  and 

name. 
International 


burgee 


with 


signal 


code. 


Plugs 


bung 


hole ;   2,   with 


Boat  Outfit. 

Ash  oars,  thole  pins  or  rowlocks 
Rudder  (lanyard). 
Tiller  (lanyard). 
Painter,  5  fathom  line. 
Cable,  20  fathom  line. 
Boat  hook. 
Water  breakers. 
Bread  tank. 

for 

chain 
One  anchor. 
One  sea  anchor. 
One  bailer. 

One  mast  yard  and  sail. 
One  compass  4"  card  in  case. 
Four    oil    lanterns   to  burn   8 

hours. 
Four  oil  distributers,  1 

each. 
Twelve  boat  hatchets. 


gallon 


Specification    Headings 


G7 


Boatsioain'a  si,, res. 

Watch  tackles. 

Relieving  tackles. 

Luff  tackles. 

Spare  blocks,  double  and  single, 

assorted. 
Spare  sheaves,  for  boat  falls. 
Snatch  blocks. 
Cargo  gins. 
Deck  scrubbers. 
Wood  fenders,  with  lanyards. 
Cork  fenders,  with  lanyards. 
Marline  spikes. 
Crowbars. 
Chain  hooks. 
Chain  slings. 
Hair  crate  hooks. 
Screw  shackles. 
Pairs  of  grip-honks. 
Pairs  of  case-hooks. 
Coir  brooms  and  handles. 
Mops. 

Ballast  shovels. 
Scrapers,  triangular. 
Scrapers,  steel  file. 
Set     of     funnel     blocks     and 

boards. 
Boatswain's  chairs,  one  to  each 

mast. 
Pilot  ladder. 
Five-inch   portable   fire   engine 

pump  with  hose. 
Bath  bricks. 
Hand  spikes. 
Paint  scrubbers. 
Pairs  of  handcuffs. 
Branding  iron. 
Painl  brushes,  assorted. 
Paint  pots,  one-half  gallon. 
Squeegees,  large. 
Scraping  box,  tin. 
Sewing  palms. 
Needles. 
Beam  clamps. 
Whitewash  brushes. 


( '<iri><  lifer's  stores. 

"  Propeller  "  notice  boards. 
"Smoking''  notice  boards. 

••No  admittance"  notice  boards. 

Pump  hook,  jointed. 

Chain  punches. 

Pitch  pot,  3  gals,  and  ladle. 

Tar  bucket. 

Grindstone     and    trough,     18" 

diam. 
Shifting  spanner,  large. 
King  spanners,    to   fit    bunker 

plates,  etc. 
Keys  for  cargo  ports. 
"     "   sidelights. 
"     "   coal  ports. 
"     "    mushroom  ventilators. 
Kim  spanner  for  sidelights. 
Spanners  for   deep  tank  hatch 

bolts. 
Rail  straightener,  3'  6"  long. 
Kod  sounding  rods. 
Flexible  sounding  rods,   2'  0" 

long. 
Caulking  tools. 
Caulking  mallet. 
Spare  hatch  wedges. 
Capstan  bars  and  rack. 
Monkey  wrench. 
Wheel-house  axes,  large. 
Tools    in     chest,    with     ship's 
name     on ;     chest     and 
tools. 
One  26"  hand  saw. 
One  crosscut. 
One  auger  \\". 
One  purger  \\". 
One  adze. 
One  hammer. 
Two  top  mawls. 
Two  screwdrivers. 
One  jack  plane. 
One  hand  plane. 
Three  chisels,  assorted. 
Three  gimlets,  assorted. 


68 


The   Naval   Constructor 


Steaming  Lights. 


lamps,    "brass, 
for  electric. 

oil. 


Two  masthead 

Fort 

Starboard 

do.  do.  galvanized  iron,  for 

Two  riding  lights         i 

One  overtaking  light   >  oil. 

Three  ruby  lights         ) 

Three  black  balls. 

Spare  glasses  for  lamps,  2 

each. 
Carriers  and  halliards  for  mast- 


for 


head  and  riding  lights. 


Lamps  and  lanterns. 

"Exit"  lamps   in    passengers' 

quarters. 
Dark  lanterns  (3  for  large  ships). 
Cargo    lanterns    (12   for    large 

ships). 
White    lanterns    (2    for    large 

ships). 
Hurricane   lights    (5    for   large 

ships)      with      3      spare 

glasses. 
Lamps  for  saloon  and  officers' 

rooms  in  small  ships. 
Lamp  scissors. 
Oil  funnels. 
Lamp  wicks. 

Rockets,  signal  cannon,  to  be 
supplied  as  required  by 
U.  S.  laws,  together  with 
owner's  night  signals, etc. 

Navigating  Instruments. 

Standard  compass  and  stand. 

Ten  inch  spirit  compasses  in 
navigating  positions. 

One  spare  card. 

Boat's  compasses,  4"  card. 

Sounding  machine,  or  deep  sea 
lead  (28  lbs.),  line  and 
reel.     130  fathoms. 


Hand  lead  (16  lbs.),   line,  and 

reel,  30  fathoms. 
Pelorus. 
Clocks. 

Aneroid  barometers. 
Telescope. 
Binoculars,  marine. 
Log  slates. 
Parallel  ruler. 
Pair  dividers. 
Chart  weights. 
Foghorn. 

Tarpaulins. 

Usually  3  to  each  weather  deck 
hatch  ;  1  to  others. 

One  rubber  sheet  to  hatches  on 
which  cattle  are  carried. 

Covers  to  all  sails  and  instru- 
ments, wheels,  etc.,  in 
exposed  positions  ; 
weather  cloths  to  shelter 
passenger  decks  in  large 
passenger  ships. 

Bakery  Outfit. 

Two  biscuit  tubes. 

One  biscuit  forcer. 

One  apple  corer. 

One  bread  rasp. 

One  galvanized  bucket. 

One  buckwheat  jug. 

Six  cake  hoops. 

One  hundred  and  twenty  corn 

bread  tins. 
One  dough  knife. 
One  scraper. 
One  sugar  dredger. 
One  flour  dredger. 
Two  flour  scoops. 
One  tin  opener. 
One  casserole  mould. 
Eighteen  (quart)  jelly  moulds. 
Six  pudding  moulds  with  lids. 
Seventy-two  muffin  rings. 
One  bread  grater. 


Specification    Headings 


69 


One  nutmeg  grater. 

One  barm  can. 

One  palette  knife. 

Two  sets  cutlet  paste  cutters. 

Six  paste  brushes. 

Two  rolling  pins. 

I  me  set   of  scales,  ]    oz.   to  14 

lbs. 
One  flour  sieve. 
<  )ne  spice  box  complete. 
Twelve  bread  tins. 
Two  French  roll  tins. 
Twenty-four  open  tart  tins. 
One     hundred     and    forty-four 

patty  tins. 
Six  rice  pudding  tins. 
Six  roll  tins. 
Eighteen  sandwich  bread   tins, 

with  lids. 
Twenty-four        sponge       cake 

frames. 
One  water  can. 
Two  egg  whisks. 
One  set  icing  pipes. 
One  icing  bag. 

One  enameled  whisking  bowl. 
One  patent  egg  whisk. 
One  egg  basket. 
One  suet  machine. 
One  bread  knife. 
Twelve  large  bread  sheets. 
One  bread    prover.    galvanized 

iron,  0'  0"  x  2'  5"  x  V  5" 

with  copper  steam  pipe. 

Galley  Outfit. 

Braising    pans,     copper,     with 

wire  nets. 
Water  cans. 
Butcher's  choppers. 
Cook's  saws. 
,Tin  colanders 
Chopping  block. 
Dippers,  tin. 

Aluminum     stew     pans,     with 
handles  and  lid. 


Sauce  pans  (enameled  iron),   1 

qt.,  3  pt.,  and  2  qt. 

Oval  fish  kettle  and  lid. 

Potato  masher. 

Dog  baskets,  wicker,  tin    lined. 

Sieves,  hair  mesh. 

Sieves,  wire  mesh. 

Sauce  ladles,  small. 

Tin  opener. 

Beef  press. 

Pea  soup  masher,  tammy  sieve. 

( lopperstew  pans,  6"-16"diam., 
with  long  handles,  and 
lids  with  long  handles. 

Stock  bucket. 

Stock  pot. 

I  Omelette  pans,  copper. 

Frying  pans,  round. 

Frying  pans,  oval. 

Tormentors. 

Pokers. 

Shovels. 

Rakes. 

Gridirons,  double. 

Gridirons,  large. 

Sets  of  skewers,  assorted  sizes. 

Egg  basket. 

Glaze  pot,  copper  and  brush. 

Four-inch  basket  ladle,  wire. 

Frying  baskets,  round,  wire. 

Cook's  forks. 

Salt  box. 

Flour  box. 

Wire  gravy  strainer. 

Grill  tins. 

Two  gallon  copper  kettle. 

Jelly  bag. 

Knives.  French. 

Knives,  butcher's. 

Knives,  mincing. 

Knives,  oyster. 

Knives,  palette. 

Knives,  potato. 

Hill  of  fare  frame. 

Pie  pans,  12"  X  8",  enameled. 

Pie  pans.  8"  x  0". 


70 


The   Naval   Constructor 


Steak  tongs. 

Store  tins. 

Stove  top  hooks. 

Porridge  whisks,  strong  wire. 

Cutlet  bat. 

Vegetable  cutters. 

Vegetable  scoops. 

Brawn  moulds. 

Tongue  press. 

Pepper  dredgers. 

Hot  pot  tins. 

Plate  carriers. 

Bread  grater. 
Flour  dredge. 
Iron  ladles. 
Larding  needles. 
Trussing  needles. 
Potato  masher. 
Egg  slicer. 
Fish  slicer. 
Spoons,  iron. 
Spoons,  wood. 
Steel. 

SJiip's  Galley  Outfit. 

Mess    kids,    large,    small    and 

oval. 
Square  steamers. 
One    square    coffee    boiler    (28 

gal.)  B.  T. 
Oval  boilers  (15  gal.)  B.  T. 
Roast  tins. 

Saucepans,  iron  enameled. 
One    round    steam    boiler    (50 

gal.)  cast  iron  with  large 

brass  tap. 
Range. 
Colanders. 
Shovel. 
Poker. 

Buckets,  galvanized  iron. 
Rake. 

Tormentor. 
Large  ladle. 
Square  duff  tins. 
Chopping  block. 


Pantry  Outfit. 

Pair  butter  spades. 

Meat  choppers. 

Poultry  choppers. 

One  clock. 

Dish  covers,  B.  M. 

Egg  slicers. 

Ice  pricker. 

Jugs  (enameled),  1  gallon. 

Two  bread  knives. 

Two  carving  knives. 

Two  French  knives. 

Two  ham  knives. 

Pairs  knives  and  forks  for  poul 

try. 
Plate  covers,  tin. 
Iron  spoons,  18"  long. 
Lemon  squeezer. 
Tin  openers. 
*  Slop  receivers,  20  gallons. 
Soup  ladles. 
Soup  tureens,  B.  T. 
Steel. 

Waiter's  Carpathian. 
Wire  whisks  12"-18". 
Milk  cans  with  lid  and  spout, 

2  gallons. 
Steam  carving  table  6'  0"  x  2' 
6",  with  tin  top,  3  large, 
2    medium   and  2   small 
wells. 
Steam  egg  boiler. 
Steam  bain-marie,  4  stew  pans, 

brass  frame. 
One  coffee   boiler,    10   gallons, 

E.P. 
One   hot   water  boiler,    15  gal- 
lons E.  P. 
Whisking  bowl. 
Water  cooler. 

Electroplate  and  Cutlery. 

Asparagus  tongs. 
Butter  coolers. 
Cheese  scoops. 


Specification  Headings 


71 


Tea  pots,  3  pints. 
Tea  pots,  1\  pints. 
Coffee  pots,  2  pints. 
Coffee  pots,  1  pint. 
Entree  dishes,  10"  oval. 
Entree  dish  covers,  with  mov- 
able handles. 
Vegetable  dishes. 
Vegetable     dish     covers,     with 

movable  handles. 
Ice  tongs. 
Sauce  frames    (Worcestershire, 

etc.). 
Prs.  fish  carvers. 
Fish  forks. 
Fruit  forks. 
Dessert  forks. 
Pickle  forks. 
Butter  knives. 
Fish  knives. 
Dessert  spoons. 
Soup  spoons. 
Sauce  ladles. 
Soup  ladles. 
Finger  bowls. 
Ice  pails. 

Napkin  rings,  numbered. 
Prs.  nut  crackers. 
Toast  racks,  large. 
Toast  racks,  small. 
Fruit  knives. 
Mustard  spoons. 
Salt  spoons. 
Tea  spoons. 
Egg  spoons. 
Table  spoons. 
Sugar  bowls,  large, 
bowls,  small. 

"      tongs,  small. 

"      tongs,  large. 
Sardine  tongs. 
( 'ream  jugs,  large. 
Cream  jugs,  small. 
Fine  sugar  sifters,  gilt  bowls. 
Fine  sugar  bowls. 
Syrup  jugs,  hinged  lids. 


Hot  water  jugs,  1  pint 

Tureen  and  covers  for  soup,  6 

quarts. 
Tureen  and  covers  for  sauce. 
Fruit    dishes,    gilt,    huge    12" 

long. 
Fruit  dishes,  gilt,  small,  9£"long. 
Wine  corks. 
Waiters,  8",  10",  12". 
Wine  funnel. 

Glass. 

( 'elery  glasses. 

Tumblers. 

Soda  glasses. 

Champagne  glasses. 

Claret  glasses. 

Liqueur  glasses. 

Port  and  Sherry  glasses. 

Cocktail  glasses. 

Bedroom  tumblers. 

Pickle  jars. 

Glass  dishes,  small  oval. 

"         "       large  oval. 

"         "       large  round. 

"         "       small  round. 

"         "        ground    glass    for 
ice  cream. 
Water  decanters,  saloon. 
Water  decanters,  bedroom. 
Salt  casters. 

Pepper  casters,  E.  P.  tops. 
Red  pepper  casters,  E.  P.  tops. 
Salad  bowls. 

China. 

Dessert  plates. 
Teacups,  afternoon. 
Tea  saucers,  afternoon. 

Earthenware. 

Breakfast  cups  and  saucers. 

Tea  cups  and  saucers. 

After-dinner    coffee    cups     and 
saucers. 


72 


The   Naval   Constructor 


Egg  cups,  d.  e. 
Dinner  plates. 
Soup  plates. 
Cheese  plates 
Slop  basins. 
Jardinieres,  large. 
Jardinieres,  small. 
Chambers,  bedroom. 
Milk  jugs. 

Linen. 

Two  prs.  sheets  to  each  berth. 
One  pr.  blankets  to  each  berth. 
One  bed-spread  to  each  berth. 
Two    pillow    cases     to     each 

pillow. 
Two  pillows  to  each  berth. 
One  mattress,  over  spring  mat- 
tress. 
One  mattress  cover. 
Three  sets  tablecloths. 
Napkins. 

Table  covers,  baize,  red,  etc. 
Glass  cloths. 
Towels,  pantry. 

' '       passenger,  four  to  each . 

"       officers,  four  to  each. 

"       lavatories. 


Towels,  bath. 
Dusters. 

Covers  for   saloon   chairs   and 
settees. 

General  Stores. 

Spring  balance. 

Scales  and  weights. 

Handy  billy. 

Brooms. 

Brushes,  banister. 

Dustpans  and  brushes. 

Shoe  brushes. 

Buckets. 

Mops. 

Cuspidores  and  linings. 

Dinner  bell. 

Cork  screws. 

Knife  board. 

Table  gong. 

Deck  chairs. 

Wicker  chairs. 

Blotting  pads. 

Bibles,  etc. 

Chess  men,  etc. 

Library  books. 

Printing  press. 


Freeboard  73 


CHAPTER  IV. 
FREEBOARD. 

A  very  close  approximation  to  the  freeboard  a  vessel  is  entitled 
to  under  the  Board  of  Trade  Freeboard  Rules  may  be  obtained 
from  the  following  notes  and  tables  of  their  requirements. 

The  tables  are  made  up  for  full  scantling,  spar  and  awning  deck 
vessels,  allowances  being  granted  to  vessels  intermediate  in  strength 
to  the.se  grades  as  determined  by  Lloyd's  188-3  Rules  ;  for  example, 
a  vessel  stronger  than  an  awning  or  hurricane  decker,  but  yet  not 
equal  to  the  requirements  for  a  spar  decked  vessel,  would  receive 
as  a  reduction  in  freeboard  a  percentage  of  the  difference  between 
the  freeboard  per  Tables  B  and  that  by  Table  C,  such  percentage 
depending  on  the  excess  strength  over  the  awning  deck  require- 
ments. Similarly  a  vessel  coming  between  a  spar  decker  and 
a  full  scantling  vessel,  would  receive  a  percentage  of  the  difference 
between  the  freeboards  by  Tables  A  and  B.  Pull  scantling  vessels 
also  receive  allowances  on  account  of  erections  on  deck,  excess 
sheer  and  round  of  beam.  Spar  and  awning  decked  vessels  receive 
no  allowances  (except  in  the  case  of  spar  deckers  having 
strengthened  bridge  houses  extending  over  §  or  more  of  the  length) 
on  these  accounts,  but  are  penalized  for  deficiency  in  sheer  and 
round  of  beam  as  are  full  scantling  vessels.  In  order  to  obtain 
the  full  allowances  for  erections,  poop,  raised  quarter  decks, 
bridges  and  forecastles  must  be  enclosed  by  efficient  bulkheads. 

Tn  ascertaining  the  freeboard  it  is  necessary  that  the  following 
points  be  known,  at  any  rate,  with  a  fair  degree  of  accuracy. 

Coefficient  of  Fineness. — This  coefficient  is  that  of  the 
under  deck  tonnage,  the  deck  worked  to  being  the  upper  deck  in 
full  scantling  vessels,  spar  deck  in  spar  deckers,  and  main  deck 
in  awning  deckers.  The  tonnage  as  calculated  is  to  include  all  the 
spaces  below  such  deck. 

The  coefficient  is  found  from  the  formula: 

U.D.T.  x  100 
~L  ■    i:  x2T' 

where  V.  D.T.  =  under  deck  tonnage, 

where  L,  B,  and  D  =  the  registered  dimensions  of  the  vessel.   D 
b  ing  the  depth  of  hold. 

This  coefficient  is  intended  to  be  an  accurate  comparison 
between  vessels,  and  is  standard  for  vessels  with  ordinary  fh 


and  framing,  so  that  small  corrections  have  to  be  made  for  vessels 
having  partial  or  complete  double  bottoms,  deep  framing,  etc.,  in 
order  that  the  coefficient  used  may  express  the  condition  of  affairs 
reduced  to  the  basis  of  the  standard  type  of  ships. 

Dimensions.  —  In  using  the  tables,  the  length  and  depth 
referred  to  are  iu  all  cases  the  length  on  the  load  water  line  and 
the  depth  moulded,  the  only  place  in  which  the  registered 
dimensions  appear  being  as  above.  The  depth  moulded  is  from 
the  top  of  the  keel  to  the  top  of  deck  beam  at  side,  measured 
at  the  middle  of  the  vessel's  length.  The  deck  beam  to  which  the 
measurement  is  taken  will  vary  with  the  type  of  vessel,  being  the 
upper  deck  in  shelter  deck  and  full  scantling  vessels  and  the  main 
deck  in  spar,  awning  or  hurricane  deckers. 

This  is  the  depth  used  in  applying  the  tables,  and  holds  good  in 
all  cases  except  that  of  a  full  scantling  vessel  with  a  steel  upper 
deck  unsheathed  with  wood,  having  erections  covering  less  than 
40  per  cent  of  the  vessel's  length,  in  which  case  the  moulded 
depth  is  reduced  by  the  rule  thickness  of  a  wood  deck  and  the 
reduced  depth  used  in  applying  the  tables.  In  all  other  cases  of 
steel  decks  unsheathed  with  wood  the  usual  thickness  of  a  wood 
deck  is  deducted  from  the  freeboard,  the  proportion  in  vessels 
having  more  than  40  per  cent  and  less  than  70  per  cent  covered 
varying  from  40  per  cent  to  100  per  cent  of  the  thickness  of  the 
wood  deck. 

The  freeboard  found  from  the  tables  is  measured  from  the  top 
of  the  wood  or  steel  deck  as  the  case  may  be,  though  in  the  final 
assignment  a  correction  will  be  made  for  the  statutory  deck  line, 
which  correction,  however,  need  not  concern  the  naval  archi- 
tect m  estimating  the  draft,  as  it  does  not  influence  the  final 
position  of  the  disc  in  its  height  above  keel.  The  freeboard  of 
vessels  which  habitually  trim  very  much  by  the  stern  will  have  to 
receive  special  consideration.  The  tables  are  made  up  for  vessels 
having  a  proportion  of  length  divided  by  depth  equal  to  12, 
this  depth  being  to  the  upper  deck  in  full  scantling  vessels,  spar 
deck  in  spar  deckers,  and  main  deck  in  awning  or  hurricane 
deckers  ;  any  variation  from  these  proportions  will  have  to  be 
corrected  for  as  indicated  in  the  footnote  to  each  table,  greater 
length  causing  an  addition  to  freeboard,  and  lesser  length  a  corre- 
sponding reduction. 

The  tables  are  based  on  the  assumption  that  the  proportions  of 
breadth  to  depth  are  such  as  to  secure  good  seaworthiness,  and  if 
such  is  not  the  case  the  freeboard  will  be  liable  to  special 
consideration. 

Deck  erections  on  full  scantling  vessels  receive  an  allowance  on 
account  of  the  contribution  they  afford  to  the  reserve  buoyancy, 


but  such  erections  must  be  an  integral  part  of  the  structure  and 
closed  by  efficient  bulkheads.  Wooden  or  steel  houses  are  not 
considered  as  erections,  only  poops,  raised  quarter  decks,  bridges, 
raised  foredecks  and  forecastles  being  classed  as  such.  The 
machinery  openings  must  lie  protected  by  one  of  these  erections 
if  the  full  allowance  is  to  be  claimed  for  such  erection.  The 
allowance  is  always  a  percentage  of  the  difference  between  the 
freeboard  by  Table  A  as  a  flush  decked  ship  and  that  by  Table  C 
3  a  fully  covered-in  ship.  In  vessels  having  top  gallant  forecastles, 
!'iig  poops  or  raised  quarter  decks  connected  with  bridge  houses, 
the  latter  closed  by  an  efficient  bulkhead  at  the  fore  end  and 
entered  from  the  top,  may  have  a  deduction  varying  from  50 
per  cent  of  the  difference  between  freeboard  by  Table  A  (after  cor- 
rection for  sheer)  and  Table  C  in  vessels  having  erections  covering 
00  per  cent  of  the  vessel's  length  to  90  per  cent  of  the  difference  in 
■  essels  having  erections  covering  96  per  cent  of  the  length. 

The  raised  quarter  deck  should  be  4'  0"  in  height,  otherwise 
there  will  be  an  addition  varying  with  the  decrease  in  height. 
The  minimum  height  for  poops,  bridges  and  forecastles  is  6'  0". 

When  the  erections  consist  of  a  poop  bridge  and  topgallant 
forecastle,  the  allowance  varies  from  25%  the  difference  between 
Table  A,  after  correction  for  sheer  and  length,  and  Table  C,  after 
correction  for  length,  in  vessels  having  30%  of  the  length  covered, 
to  70%,  the  difference  in  vessels  having  80%  of  the  length  covered. 
When  the  erections  consist  of  a  topgallant  forecastle  and  bridge 
house  only,  16%  the  difference  between  Table  A  after  correction 
for  sheer  and  length,  and  Table  C  after  correction  for  length,  in 
vessels  having  20%  covered  to  37%  in  vessels  50%  covered.  When 
the  erections  consist  of  a  poop  and  topgallant  forecastle  only,  the 
deduction  from  Table  A  after  correction  for  length  is  from  8%  of 
the  freeboard  in  vessels  25%  covered  to  12%  in  vessels  50%  covered. 
When  a  vessel  is  fitted  with  a  topgallant  forecastle  only,  the  al- 
lowance is  one  half  that  which  would  be  granted  if  she  were  lifted 
with  a  poop  of  the  same  length  ;  similarly  a  vessel  with  a  poop  only, 
would  have  half  the  allowance  she  would  get  if  fitted  with  a  fore- 
castle of  the  same  length. 

Sheer.  —  In  flush  deck  vessels  and  in  vessels  havin?  enclosed 
poop,  bridge,  and  forecastle,  the  sheer  at  side  is  measured  at  the 
stem  and  sternpost,  and  in  vessels  having  poop  and  forecastle  at  \ 
the  vessel's  length  from  ends.  The  mean  sheer  is  the  sum  of  the 
end  sheers  divided,  by  2. 

In  flush  deck  vessels,  the  standard  mean  sheer  is  20"  for  vessels 
100  ft.  long,  30"  for  vessels  200  ft.  long,  up  to  70" in  vessels  600  ft.  Ion 

In  vessels  having  poops  and  forecastles,  the  standard  mean  sheer 
is  14"  for  vessels  100  ft.  between  the  points  of  measurement,  22" 


76 


The   Naval   Constructor 


for  vessels  200  ft.  long,  up  to  54"  for  vessels  600  ft.  long  between 
the  points  of  measurements.  From  these  figures  diagrams  can 
readily  be  drawn  if  required. 

The  difference  between  the  actual  mean  sheer  and  standard 
mean  sheer  is  divided  by  4,  this  figure  being  added  to  or  sub- 
tracted from  the  freeboard  according  as  the  sheer  is  below  or 
above  the  standard  respectively.  Spar  and  awning  decked  vessels 
are  not  corrected  for  excess  of  sheer,  but  are  penalized  for  defi- 
ciency. The  sheer  line  must  be  gradual  to  enable  vessels  to 
obtain  the  maximum  allowance. 

Round  of  Beam.  — The  Tables  are  based  on  a  standard  round 
of  beam  of  \"  for  every  foot  of  beam,  and  whenever  this  rule  is  de- 
parted from,  the  difference  in  inches  between  the  actual  and  the 
standard  camber  is  divided  by  2,  and  this  figure  added  to  or  sub- 
tracted from  the  freeboard  according  as  the  camber  is  less  or 
greater  than  the  standard. 

Miscellaneous  Allowances. — Vessels  loading  in  fresh  water 
may  load  as  much  deeper  as  they  will  rise  when  passing  from  fresh 
to  salt  water.  Similarly,  vessels  navigating  a  long  stretch  of  inland 
or  land  locked  water  may  load  as  much  deeper  as  they  will  rise 
due  to  the  weight  of  fuel  burnt  and  stores  consumed,  whilst  navi- 
gating such  stretch. 

Well-decked  vessels  of  the  modern  type  having  erections  extend- 
ing over  70%  of  the  length  with  strengthened  bridge  fronts,  25% 
freeing  port  area  above  the  rule  requirements,  and  hatchway 
coamings  at  least  30"  high,  may  have  an  allowance  of  ^  the  sum- 
mer freeboard  after  all  other  deductions  are  made  ;  such  allow- 
ance may  not  exceed  2".  These  vessels  having  erections  covering 
85%  of  the  length,  the  bridge  house  alone  covering  40%,  may  have 
an  allowance  of  from  2\"  to  3i"  after  all  other  deductions  are 
made,  provided  that  the  erections  are  strengthened  in  accordance 
with  Section  44  of  Lloyd's  Rules  ;  such  vessels  are  not  entitled  to 
the  allowance  previously  noted  for  strengthened  bulkheads,  etc. 

Standard  freeing  port  area  may  be  found  in  Lloyd's  Rules, 
Section  31,  as  reproduced  below  :  — ■ 


Length  of  Bulwarks 
in  Well  in  Feet. 

Freeing  Pokt  Area 

on  Each 
Side  in  Square  Feet. 

30  feet 
40  feet 
50  feet 
60  feet 

9.5 
10.5 
11.5 
12.5 

65  ft.  and  above,  1  sq.  ft.  to  each  5  ft.  of  bulwark. 

Freeboards 


77 


SKETCHES  ILLUSTRATING  THE  DIFFERENT  TYFES  OF  VESSELS 


TO  WHICH  FREEBOARDS  ARE  ASSIGNED 


NO.1 


FlUSH  DECK    VESSEL. 
ENGINE   &_BpuER_  CASINGS.  MAm  DEC*»_. ' 


TRANVERSE 
SECTIONS 


NO.2 


VESSELS   HAVING  MONKEY  FORECASTLE.    BRIDGE  HOUSE,  AND  HOOO  FOR 

*NCHOB_P|cK 


THE  PROTECTION  OF  STEERING  GEAR. 
H^no  B.D. 

r-s < 


i: 


VESSEL  HAVING  TOP-GALLANT  FORECASTLE,  BRIDGE  HOUSE,  AND  POOP. 

F 


NO. 3     7 


BRIDGE    HOUSE 

WITH    IRON    BULK" 

HEAD   AT   END 


NO.4 


VESSEL    HAVING  TOP    GALLANT  FORECASTLE.  BRIDGE  HOUSE,  AND  A 
SHORT  RAISED    QUARTER  DECK. 

R.Q.D. 


BRIDGE   HOUSE — ^ 
AMIDSHIPS 
SHORT   RAISEOl 
QUARTER   DECK    ^" 


VESSEL    HAVING  TOP    GALLANT  FORECASTLE,  WITH  A  LONG  POOP  AND 
BRIDGE  HOUSE  COMBINED.  KNOWN  ASA''  WELL  DECKED  VESSEL'  ' 


B.D. 


L 


LONG  POOP  A 
BRIDGE    HOUSE    COM- 
BINED WITH    IRON 
BULKHEAD   AT   ENO 


Figs.  18-23. 


.n 


■   ne     r^rkr    v. 


UUMI  UL  LU1 


NO. 6 


VESSEL  HAVING  TOP-GALLANT  FORECASTLE    WITH  A  LONG  RAISED 

QUARTER  DECK  AND    BRIDGE    HOUSE    COMBINED  ALSO  KNOWN  AS  A  WELL 
DECKED  VESSEL  R    q 


TRANVERSE 
SECTIONS. 

LONG   RAISED 
QUARTER    DECK 
EXTENDING  TO 

PRIDCE 
HOUSE 


'SHADE  DECKED  VESSEL'THIS  TYPE  OF  VESSEL  HAS  A    CONTINUOUS  UPPER- 
DECK   OF  LIGHT  CONSTRUCTION  AND  WITH    OPENINGS   IN  THE  SIDES. 


NO. 7 


«HADE    DECK. 


|j|jlj;|||!j|l!l;|||!iii! 


NO. 8 


AWNING  DECKED  VESSEL'THIS  TYPE  OF  VESSEL  HAS  A  CONTINOUS   UPPER 
DECK  OF  LIGHTCONSTRUCTION  AND  THE  SIDES  COMPLETELY  CLOSED  ABOVE 

AWNING    OEC_K_ 


THE  MAIN  DECK- 
^Awning  DECK 


ENGINE  .*    BOILER    CASINGS. 
A 1 

'   .       '.   "'■■■.,'■   '■:ii<T!^!li!©W!!;!j!illl!|IiI 


MAIN    DECK 


NO. 9 


'SPAR  DECK  VESSEL"THIS  TYPE  OFVESSEL  IS  CONSTRUCTED    WITH  THE 
SCANTLINGS  ABOVE   THE  MAIN  DECK  HEAVIER  THAN   IN  An"awNING  DECKED' 

VESSEL  BUT  NOT  SO   HEAVY  AS  IN  A  "THREE  DECKED  VESSEL" 

B.D. 

SPAR    DECK 


BRIDGE    HOUSE 
SPAR   UECK. 

< 


NO. 10 


TURRET  DECK  VESSEL 
ENGINE    &    80ILER   CASINGS. 


-  *-..  ,;  -.::-^.-  : 


TURRET 

m 


NO. 11 


"V — 


/TRUNK 


__ 


TRUNK  DECK  VESSEL 

B.D 


^7~ 


TRUNK 


TRUNK 


Pigs. 


rTerooaras 


Table  A.  —  Freeboards  for  Full  Scantling  Freighters. 


M< •  i •  1. 1 1 1  i>  Dei* in. 


Length  <>v  L.W.L. 


Coefficient  =  6 

.76 

.80 

11  .82 

Correction  in  inches 
for  a  change  of  10 
ft.  in  length 
Deduction  in  inches 
for  summer  voy- 
ages     .... 


"" 

7'0" 

72  Ft. 

84  Ft 

-8" 

-10" 

-84 

-101, 

-9 

-11 

-9.V 

-in 

-9\ 

-Hi 

J  0.7 

0.8 

j,0 

1.0 

8'  0"      9'  0" 


96  Ft 


l'O" 

1  <»', 
i  r 

1    H 


ICO"     n'o"   lyo" 


l<»s!:.    1-jnFt. 


I'o' 


r  r 


l  2;  i  i  p. 

1  3"  1  5" 

1   3'.  1  •".' 

1  li  I  1  3V  1  b\ 


132  Ft. 


ns 


0.8       0.8 


1.0       1.0 


1.0 


1'6" 

1  i;i 

1  7" 
1  7^ 

1   71 

0.9 

l.o 


Ml  I'l 


1'8J' 
I  9 

1  '.'l 
1  10 
1  10 

0.0 
1.0 


Miti.dkd  Depth. 


Length  <»n  l.w.l. 


CoeflB  :ient  =  .68 

.72 

.76 

.80 

.82 

1    Tiection  in  inches 

for  .t  change  of  10 

ft.  in  length      .    . 

Deduction  in  inches 

for   summer   voy- 


ages 


lyo" 

14'  0" 

15' 0" 

Iff  0" 

17'  0" 

18'  0" 

156  Ft. 

168  Ft. 

180  Ft. 

102  Ft. 

204  Ft. 

216Ft. 

I'll" 

2'H" 

2'  4" 

2'  7" 

2' 10" 

3'1" 

1  1H 

2  2 

2  5 

2  8 

2  11 

3  2 

2  0 

2  3 

2  6 

2  9 

3  0 

3  3 

2  1 

2  Sh 

2  6* 

2  9} 

3  1 

3  4i 

2  1 

2  4 

2  7 

2  10 

3  n 

3  5 

|  0.9 

1.0 

1.0 

1.0 

i.i 

1.1 

),0 

1.5 

1.5 

1.5 

2.0 

2.0 

19' 0" 
228  Ft. 

3'  4" 
3  5£ 
3  6J 
3  8 
3  8J 

1.1 


2.0 


Moulded  Depth. 


Length  on  L.WX. 


Coefficient  =  .68 

.72 
.76 

.80 
"               .82 
Correction  in  inches 
for  a  change  of  10 
tt.  in  length      .     . 
Deduction  in  inches 
tor   summer   voy- 
ages       


20' 0" 


240  Ft 


3  8| 

3  10 

3  11. I 

4  0  " 

I" 

2.5 


21'  0" 


252  Ft 


3'ir 

4  0 
4  H 
4  3 

4  3^ 

1.2 
2.5 


22' 0"    23' 0" 


264  Ft, 


4'2V 
4  4" 

•"'■ 
7" 

n 


276  Ft. 


4'6J" 


8 
9i 
11 
111 


1.2        1.2 


2.5       3.0 


24'  0" 

25' 0" 

288  Ft. 

300  Ft. 

4'ior 

5'3r 

50 

5  5 

5H 

5  6£ 

53 

5  8 

54 

5  9 

1.3 

1.3 

3.0 

3.5 

26'  <y 


312  Ft. 


W  8" 

5  9i 

5  11 

6  0£ 
6  \\ 

1.4 


3.5 


80 


The   Naval   Constructor 


Table  A.  —  Freeboards  for  Full  Scantling  Freighters. 


Moulded  Depth. 

27/0// 

28'  0" 

29' 0" 

30'  0" 

31'  0" 

32' 0" 

33' 0" 

Length  on  L.W.L. 

324  Ft. 

336  Ft. 

348  Ft. 

360  Ft. 

372  Ft. 

384  Ft. 

396Ft. 

Coefficient  =  .68 

6'0h" 

6'5*" 

6,10i,/ 

7/3*'/ 

779" 

W1\" 

8'7" 

.72 

62 

6  7i 

71 

76 

7  11* 

85 

8  9* 

.76 

6  4 

6  9i 

73 

78 

81* 

87 

90 

.80 

6  5* 

611 

75 

7  10* 

84 

8  9i 

9  2* 

.82 

6  6* 

70 

76 

7  11* 

85 

8  101 

9  3* 

Correction  in  inches 
for  a  change  of  10 
ft.  in  length      .     . 

Deduction  in  inches 
for   summer  voy- 

1" 

J  4.0 

1.4 

4.0 

1.5 

4.5 

1.5 
4  5 

1.6 

5.0 

1.6 
5.0 

1.6 

5.5 

Moulded  Depth. 

34'  0" 

35'  0" 

36'  0" 

37'  0" 

38' 0" 

39' 0" 

468  Ft. 

.  .  . 

Length  on  L.W.L. 

408  Ft. 

420  Ft. 

432  Ft. 

444  Ft. 

456  Ft. 

.  .  . 

Coefficient   =.68 

W 

9'5" 

9'9" 

10,1'/ 

10'5" 

10'9" 

"                .72 

9  2i 

9  7* 

911* 

10  3* 

10  8 

110 

.76 

95 

910 

10  2* 

10  6* 

1011 

113 

.80 

9  7* 

10  01 

10  5 

10  9 

111* 

11  5* 

.82 

98i 

101* 

10  6* 

10  10* 

113 

117 

Correction  in  inches 
for  a  change  of  10 
ft.  in  length     .     . 

Deduction  in  inches 
for  summer  voy- 

1" 

J6.0 

1.7 
6  0 

1.7 

6.5 

1.7 
6.5 

1.7 
7.0 

1.7 

7.0 

.  .  . 

) 

Mouxded  Depth. 

40'  0" 

42'  0" 

44/0// 

46'  0" 

48'  0" 

50'  0" 

.  .  . 

Length  on  L.W.L. 

480  Ft. 

504  Ft. 

528  Ft. 

552  Ft. 

576  Ft. 

600  Ft. 



Coefficient   =.68 

ll'l" 

11'8£" 

12/3*,/ 

12'101,/ 

13'5" 

13a  i" 

"                .72 

114 

11  Hi 

12  7 

13  2 

13  81 

14  3 

.  .  . 

.76 

117 

12  21 

12  10 

13  6 

14  01 

14  6t 

.80 

1110 

12  5i 

13  1* 

13  9 

14  31 

1410 

.  .  . 

"               .82 

11  1H 

12  7* 

13  3* 

13  10* 

14  5* 

15  0 

Correction  in  inches 
for  a  change  of  10 
ft.  in  length      .     . 

Deduction  in  inches 
for   summer  voy- 

|  7.5 

1.7 

8.0 

1.7 

8.5 

1.7 
9.0 

1.7 
9.5 

1.7 

9.5 

.  .  . 

] 

Freeboards 


81 


Table  B.  —  For  Spar  Deck  Freighters. 


Moulded  Depth. 

13'  0" 

14'  0" 

WW 

WW 

17' 0" 

WW 

I.i  \<.  in  ox  L.W.I.. 

240  Ft. 

252  Ft. 

204  Ft. 

278  Ft. 

288  Ft. 

300  Fl. 

Coefficient  =  .68 

5'5" 

57" 

5'9" 

5'11" 

0'1  \" 

6'4" 

70 

66 

58 

510 

00 

62$ 

0  5* 

.76 

5  7 

5  9 

511 

61 

6  3  \ 

6  6$ 

"               >sn 

5  8 

5  10 

60 

62 

64$ 

071 

.82 

5  8$ 

510$ 

60$ 

<i2* 

65 

6  8 

<  lorrection  in  inches 

) 

t.ir  a  change  of  10 

•'•' 

.!) 

.9 

1.0 

1.0 

1.0 

ft.  in  length      .     . 

I 

I  deduction  in  Inches 

|  ._,„ 

for  summer  voj- 

2.0 

2.5 

2.5 

3.0 

3.0 

) 

Moulded  Dep  1 11. 

10'  0" 

•jo-  0" 

21'  U" 

J_''  0" 

23' 0" 

24'  0" 

I. IN..  II!   <>N   L.WJJ. 

312  Ft. 

324  Ft. 

336  Ft. 

348  Ft. 

360  Ft. 

372  Ft. 

Coefficient  =  .08 

o'7.r 

6'11" 

'  -j 

7'7" 

7iir 

8'41" 

.72 

69 

7  0$ 

74 

7  8V 

81 

8  6 

.70 

0  10 

71$ 

7  5$ 

7  10 

82$ 

87V 

.80 

(ill 

7  2  | 

76$ 

711 

8  3$ 

8  8^ 

"               .82 

6  1 1 $ 

7  3 

7  7 

711$ 

84 

8  9i 

Correction  in  inches 

) 

for  a  change  of  lu 

1.1 

1.1 

1.1 

1.2 

1.2 

1.3 

ft.  in  length      .     . 

1 

Deduction  in  inches 

j  3.5 

for  summer  vuy- 

3.5 

4.0 

4.5 

4.5 

5.0 

J 

BfouiiDBD  Depth. 

2.V  0" 

26'  0" 

27'  0" 

28'  0" 

29'  0" 

S^O" 

Length  ok  L.W.L. 

384  Ft. 

396  Ft. 

408  Ft. 

420  Ft. 

432  Ft. 

444  Ft. 

Coefficient   =  .08 

8'9|" 

9'2\" 

9'8" 

10'2" 

iow 

ii'3" 

.72 

811 

94$ 

9  10 

104 

10  10$ 

11  5 

.76 

9  0i 

96 

101) 

106 

1101 

11  7 

.80 

92 

97* 

10  H 

10  7V 

112 

119 

«               .82 

93 

98V 

10  21 

10  8$ 

11  3 

11  10 

eorrection  in  inches 

'.,: 

for  ;t  change  of  10 

1.3 

1.4 

1.4 

1.5 

1.6 

ft.  in  length      .     . 

1 

Deduction  in  inches 

j  B.6 

h>r   summer   voj- 

•  ).-> 

6.0 

6.0 

0.5 

0.5 

J 

82 


The   Naval   Constructor 


Table  C.  —  Freeboards  for  Awning  Deck  Freighters. 


Moulded  Depth. 

14' 0" 

15' 0" 

W0" 

WW 

18' 0" 

19' 0" 

*  20'  W 

Length  on  L.W.L. 

168  Ft. 

180  Ft. 

192  Ft. 

204  Ft. 

216  Ft. 

228  Ft. 

240  Ft. 

Coefficient   =  .68 

ro" 

l'l" 

1'2" 

1  '31" 

1'6" 

1'7" 

1'9" 

.72 

101 

1  H 

1  3 

14i 

16 

18 

1  10 

.76 

1  1 

12 

13i 

1  5 

161 

18i 

1  10i 

"               .80 

m 

12* 

14 

151 

1  7 

19 

1  Hi 

Correction  in  inches 

) 

•        * 

for  a  change  of  10 

.5 

.5 

.0 

.5 

.5 

.6 

.6 

ft.  in  length     .     . 

J 

Deduction  in  inches 

) 

for  summer  voy- 

2.0 

2.0 

2.0 

2.5 

2.5 

3.0 

3.5 

ages      

) 

Moulded  Depth. 

21/0// 

22'  0" 

23' 0" 

24/0// 

25' 0" 

26' 0" 

27'  0" 

Length  on  L.W.L. 

252  Ft. 

264  Ft. 

276  Ft. 

288  Ft. 

300  Ft. 

312  Ft. 

324  Ft. 

Coefficient   =.68 

mr 

2,2|// 

2-sr 

2/8i// 

3'0i" 

3'4§" 

O  i^2 

.72 

2  0i 

2  3i 

2  6i 

2  91 

31i 

3  5i 

310J 

"                .76 

21 

24 

27 

2  101 

32i 

37 

40 

"               .80 

22 

25 

28 

2  1H 

3  3i 

38 

4  1 

Correction  in  inches 

) 

fur  a  change  of  10 

.6 

.6 

.6 

.6 

.7 

.7 

.7 

ft.  in  length    .     . 

1 

Deduction  in  inches 

) 

for  summer  voy- 

3.5 

4.0 

4.0 

4.5 

5.0 

5.0 

5.5 

) 

Moulded  Depth. 

2S/0" 

29'  0" 

WW 

31' 0" 

32' 0" 

33'  W 

34' 0" 

Length  on  L.W.L. 

336  Ft. 

348  Ft. 

360  Ft. 

372  Ft. 

384  Ft. 

396  Ft. 

408  Ft. 

Coefficient  =  .('8 

4'2r 

4'7i" 

5'1" 

5'6§" 

6'0" 

6'5" 

e'lO" 

"               .72 

4  3i 

49 

5  2i 

58 

6H 

6  6$ 

6111 

"               .76 

45 

4  10 

54 

5  9i 

63 

68 

7  1 

"               .80 

46 

4  11 

55 

5  10* 

64 

69 

7  2i 

Correction  in  inches 

) 

for  a  change  of  10 

.7 

.7 

.8 

.8 

.8 

.8 

.8 

ft.  in  length      .     . 

) 

Deduction  in  inches 

J5.5 

for    summer  voy- 

6.0 

6.0 

6.0 

6.5 

6.5 

6.5 

J 

Notes  on  Tables  83 


Notes  on  Tables  A,  B,  and  C. 

Table  A.  —  Moulded  depth  is  depth  measured  at  the  middle  of 
the  length  from  the  top  of  the  keel  to  top  of  upper  deck  beam  at 
side. 

hihle  B.  —  Moulded  depth  is  the  depth  measured  from  the  top 
of  keel  to  top  of  main  deck  beam  at  side  ;  the  freeboard,  however, 
is  measured  from  the  top  of  spar  deck  at  side. 

Table  C.  — Moulded  depth  is  depth  to  top  of  main  deck  beams, 
and  the  freeboard  also  is  measured  from  this  deck.  To  obtain  the 
freeboard  for  vessels  of  greater  depth  than  34'  0",  a  deduction  is 
made  from  the  freeboard  of  the  same  vessel  under  Table  A.  This 
deduction  varies  with  the  coefficient  of  fineness,  and  is  as  follows  : 

Coefficient  =  .68,  then  deduction  =  2' 2". 
"  =  .72      "  "  =  2' 3". 

»  =.76      "  "  =  2' 4". 

"  =.80      "  "  =2' 5 


'/ 


The  correction  for  a  change  of  lO'O"  length  =  .8". 

The  freeboard  of  vessels  of  depths  and  coefficients  of  fineness 
intermediate  to  those  given  in  the  tables  is  obtained  by  interpola- 
tion and  not  by  working  to  the  coefficient  next  below. 

Similarly,  the  correction  for  variations  in  length  is  obtained  by 
interpolation  if  the  vessel  in  question  comes  between  two  grades. 
This  remark  also  applies  to  the  deduction  for  summer  voyages. 

Vessels  of  and  under  330'  0"  in  length  require  an  extra  free- 
board of  2"  more  than  the  usual  winter  freeboard  when  trading  in 
the  North  Atlantic  during  the  winter  months. 

Let  Length  of  vessel =262/ 

Tabular  length =  252' 

Difference =    10' 

10X1.2      „,, 
.-.  Correction  = —  =  1  ]-  , 

which  will  be  added  to  freeboard  as  vessel  is  longer  than  tabular 
length. 

The  freeboard  given  by  the  tables  is  the  winter  freeboard  in 
saltwater;  the  amount  below  given  as  a  deduction  for  summer 
voyages  is  to  be  deducted;  the  summer  freeboard  being  the  one 
which  is  worked  to  in  designing  a  vessel  to  a  given  draught. 

In  the  case  of  vessels  bavin-  erections  on  deck,  the  deduction 
for  summer  voyages  is  proportionate  between  thai  given  in  Tables 
A  and  C  ;  the  proportion  varying  directly  as  the  percentage  of  the 

ogth  covered  by  erections,  as  given  on  page  74. 

Freeboard  of  a  full  scantling  steamer  having  no  erections  on 


84  The   Naval   Constructor 


deck,  of  full  scantling  to  the  upper  deck,  8"  excess  mean  sheer, 
wood  deck  and  standard  round  of  beam. 

Moulded  dimensions      =  150' 0"  x  ■24'  0''  x  14' 0". 
Under   deck   tonnage 


coefficient 

=  .68. 

Freeboard  Table  A  at 

.08=                  2'  \\" 

Correction  for  sheer 

8                             2" 

~4"              nil"' 

Correction  for  length 

18x1.0           -If". 
10                 l'9j" 

Winter  freeboard 

=  l'9f", 

Summer  freeboard 

=  l'8i", 

=  distance  of  centre  of  disc  below 

top  of  wood  deck. 

Wood  deck 

=         3" 

Moulded  depth 

=  14'0" 

14'  3" 

Freeboard 

=    1'8±" 

Moulded  mean  draught 

=  12' Of", 

which  is  the  maximum  the  vessel  could  be  loaded  to  under  these 
freeboard  rules. 

Freeboard  of  a  full  scantling  steamer  having  a  poop  bridge 
and  forecastle,  disconnected,  but  all  efficiently  enclosed,  0"  excess 
mean  sheer,  iron  deck  and  2"  too  little  round  of  beam. 

Moulded  dimensions  =  300' 0"  X  30' 0"  x  21'  0". 
Under  deck  tonnage  coefficient  =  .70. 
Erections  cover  50%  of  the  vessel's  length. 

Freeboard  Table  A    .70=  4'  1J" 

Correction  for  sheer        =  — = 


Correction  for  length 


Allowance  for  deck  erections 


6 
4~ 

n 

48  x  1.2 
10 

4'  0" 
+  5f" 

4'  5f" 

Vessel  50%  covered  =  40%  difference, 
Table  A,  corrected  for  length  and  sheer 

=  4'  5f ", 
Table  C,  corrected  for  length   =2' 4", 
Difference  =2' If", 


Notes  on  Tables  85 

40% of  26.75  =  10.3=  10}"  -    10}" 

3'  7*" 

Correction  for  round  of  beam  =s  —  =  +1 

2 


3'  8  J" 
Correction  for  iron  deck  =     —       If 

3'  Of" 

Winter     freeboard  =    3'6f", 

Summer  freeboard  =    3'  31", 

Moulded  depth        =  21'0j"    (J"  for  stringer), 

Freeboard  =    3'  3£"  to  centre  of  disc. 

Moulded  draught  =  lTSp 


Freeboard  for  a  full  scantling  vessel  having  short  poop,  raised 
quarter  deck,  bridge  house  and  topgallant  forecastle  ;  also  strength- 
ened bridge  front  and  25%  extra  freeing  port  area  in  the  well. 

Erections  covering  88%  of  the  vessel's  length  entitles  her  to  an 
allowance  of  83%,  the  difference  between  Tables  A  and  C. 

Moulded  dimensions  =  251' 6"  x  36' 6"  x  18' 4", 


Freeboard  Table  A  at  .78 

— 

3'   5" 

Correction  for  sheer 

— 

-7'- 

2  10" 

Correction  for  length 

— 

+  lf" 

2'llf 

Allowance  for  erections 

— 

-V   Of" 

I'll" 

Correction  for  iron  deck 

— 

-3V 
1'7|" 

Strong  bridge  front  and  excess 

freeing 

port  area 

= 

-w 

V   6" 

Winter     freeboard  =    1'6", 

Summer  freeboard  =    1'3J", 

Moulded  depth         =18' 4"  ' 

Stringer                     =          £" 

18'  4$" 

Freeboard                =    l'S|" 

Moulded  draught    =  17'1" 

Freeboard  of  a  spar-decked  steamer  of  strength  equal  to 
Lloyd's  1885  rules,  having  no  wood  deck  laid  on  spar  deck  and 
the ''tween  deck  height  7'0". 


86  The  Naval  Constructor 

Moulded  dimensions  =  320'  0"  X  43'  6"  x  i  ^?'  JJ"  J°  spa.r  d,ec^' 

(21  0    to  mam  deck. 

Freeboard  Table  B  at  .80       =    7'   6|" 
Correction  for  length  =      —  If" 

7'  4J" 
Correction  for  iron  spar  deck  =      —  3 J" 


7' 

ir 

Winter    freeboard 

=     7' 

iy 

Summer  freeboard 

=    6' 

9f 

Moulded  depth 

=  28' 

0" 

Stringer 

= 

r 

28'   0i" 


Freeboard  =    6'   9j" 

Moulded  draught  =  21'   3^" 


Freeboard  of   an  awning  or  hurricane  deck  steamer  of  the 
same  dimensions  as  the  spar  decker  given  above. 

Moulded  dimensions  =  320'  0"  x  43'  6"  x  21'  0"  to  main  deck. 

Freeboard  Table  C  at  .80 
Correction  for  length 


Winter    freeboard 
Summer  freeboard 

Moulded  depth 
Stringer 

Freeboard 

Load  draught  (moulded) 


— 

2' 

2" 

= 

+ 

3" 

2' 

5" 

— 

-3i" 

— 

2' 
2' 

1 1" 

= 

1' 

10" 

z 

21' 

0" 

= 

1" 

5 

21' 

or 

— 

1' 

10" 

— 

19' 

91" 
Z2 

Freeboard  of  a  steamer  having  scantlings  in  excess  of  the  awn- 
ing deck  rules,  but  not  up  to  spar  deck  rules,  the  dimensions  being 
the  same  as  in  the  two  preceding  examples. 

Dimensions  320'  0"  x  43'  6"  x  21'  0"  to  main  deck. 


Freeboard  Table  C  at  .80         =     2' 2 
Correction  for  length  =     +3 


Shelter  Deck   Steamers  87 


Allowance  for  excess  strength  : 


- 


Table  B  =  7'4f 

Table  C  =  2/l$//  (2'  5"  less  12%). 

5'  3f 

25%=i/4//  =-vr 


V  1" 

Correction  for  iron  main  deck  =     —  3^'' 

Winter     freeboard  =         9£" 

Summer  freeboard  =         6" 

Moulded  depth  =  21' 0" 

Stringer  =  \" 


21'  0£" 

Freeboard  =        6'" 

Moulded  draught  =  20'  6 J" 

It  will  thus  be  seen  that  the  same  dimensions  do  not  necessarily 
entitle  a  vessel  to  the  same  draught,  which  is  seen  to  depend  on 
strength  as  well  as  dimensions.  In  the  three  last  examples  it  is 
seen  that  the  draught  is  19' 2^"  for  the  hurricane  decker,  20'  6|" 
for  the  vessel  stronger  than  the  hurricane  decker,  and  21'  3J"  for 
the  spar  decker,  the  differences  in  these  draughts  representing 
the  extra  cargo  that  can  be  carried  less  the  extra  weight  of  hull. 
These  differences  can  be  traced  further  by  taking  a  vessel  stronger 
than  a  spar  decker,  but  nut  up  to  full  scantlings,  then  a  flush- 
decked,  full  scantling  steamer,  and  lastly  a  full  scantling  steamer 
having  erections  on  deck;  this  would  furnish  a  complete  and  very 
interesting  record. 

Shelter  Deck  Steamers. 

Under  regulations  issued  by  the  Board  of  Trade  in  March, 
1903,  shelter  deck  steamers  receive  special  treatment  in  the  assign- 
ment of  freeboard,  depending  on  the  number  and  character  of  the 
tonnage  openings.  For  vessels  with  one  such  opening  in  the 
shelter  deck,  the  freeboard  is  assigned  under  paragraph  11  of 
the  tables  ;  paragraph  12  being  used  for  vessels  having  two  or 
more  openings.  When  the  opening  exceeds  in  width  half  the 
vessel's  breadth  at  such  opening,  then  the  reduction  for  erections 
will  be  curtailed  in  proportion  to  such  width. 

Temporary  means  for  closing  the  openings  must  be  provided  in 
order  to  obtain  minimum  freeboard,  as  otherwise  a  penalty  is  en- 
forced. The  length  for  erections  is  first  taken,  assuming  each 
opening  is  an  ordinary  well,  and  the  value  of  erections  is  ascer- 


88 


The  Naval  Constructor 


tained  in  all  respects  as  for  ordinary  poops,  bridges  and  fore- 
castles, in  accordance  with  the  conditions  laid  down  in  the  tables 
as  to  bulkheads,  covering  of  engine,  and  boiler  spaces,  etc.  The 
length  as  thus  found,  plus  half  the  difference  between  that  length 
and  the  length  of  the  vessel,  is  the  length  of  erections  allowed 
when  the  openings  are  provided  with  efficient  means  for  tempo- 
rarily closing  them.  When  means  for  closing  are  not  provided, 
one-quarter  such  difference  is  to  be  taken,  and  freeing  ports  must 
be  provided  in  the  upper  'tween  decks  in  way  of  the  openings. 
An  example  of  such  a  freeboard  is  given  below  :  — 

400'  0"  X  52'  0"  x  J  83'  °"  to  uPPer  deck' 


(33' 
\4V 


0"  to  shelter  deck. 


Freeboard  Table  A,  at  .76       = 
Correction  for  sheer,  say, 


Correction  for  length 

[<^20'    >|<    1  oUk-1  b'-4< 


4x.8 


10 


9'0" 
-6" 

WW7 

_i_  3" 

+  8 

8'  6f  " 


-305- 


-50- 


K 7! 

°l    >  /id  TONNAGE 

.  -C.L 


■I- 


»/    V 


OPENING 


400 

Fig.  29. 

Allowance  for  deck  erections  : 

Poop  =  20  +  ^      =   25.00' 

Bridge  =  .  75  x  305  =  228. 75 
Forecastle  =  50'     =    50.00 

Total  =303.75 

1(400-303.75)      =   48.25 

Length  for  allow- 
ance, =  352.00 
=  88%  covered. 


Table  A      =8'   6" 
Table  C    '  =6'  8" 

8'6f" 

83%  of              V  10"=  18.25"=  1'6£" 

-1'6£" 

Winter     freeboard  = 
Summer  freeboard  = 

7'  Of 
6'5r' 

Freeboard   Marks  tor  Steamers 


89 


Statutory  allowance  above  top  of  wood  deck  =  2" 
Centre  of  disc  below  statutory' deck  line        =   6'    7' 

Draught  of  water  moulded  =  26'  lo|" 


DIAGRAMor  FREEBOARD  MARKS  tor  STEAMERS. 

(FOR  FREEBOARD  SEE  TABLES) 


STATUTORY  DECK  LINE 


UPPER  PECK  LINE  (  NOT  TO  BE   MARKED  ON  SHIPj 


THE  MARKINGS  TO  BE  CUT  INTO 
PLATING  WITH  CENTRE-PUNCH 
MARKS  AS  SHOWN  AND  PAINTED 
WHITE 


15 

Li 


METHOD  OF   MARKING  LINES 
AND  LETTERS  WITH  CENTRE- 
PUNCH. 


CENTRE  OF  DISC  TO  BB  PLACED  AT  THE 


MIDDLE  OFTHE  LENGTH  OF  THE  LOAD 
WATER  LINE 


LINES  FOR  SMALL  LETTERS    i'  THICK. 


L 


THESE  DIMENSIONS 
TO  BE  TAKEN  FROM 
1   CR.  OF  DISC  TO  TOP 
EACH   LINE 


WSK 


ST'B'D.  SIDE  SHOWN-   PORT  SIDE  SIMILAR 
Fig.  30. 


90  The  Naval  Constructor 


Freeboard  for  Sailing  Vessels. 

Freeboards  are  assigned  to  sailing  vessels  on  very  much  the 
same  principles  as  to  steam  vessels.  There  is  no  distinction 
between  winter  and  summer  draughts,  the  draught  found  from  the 
table  being  used  without  any  correction  for  voyages  in  summer. 

The  tables  for  sailing  vessels  give  less  draught  than  for  steam 
vessels  of  the  same  size,  which  difference  can  be  readily  obtained 
from  the  following  Load  Draught  Diagrams,  and  allowances  made 
for  erections  on  deck,  excess  sheer  and  round  of  beam  as  for 
steam  vessels. 

Load  Draught  Diagrams. 

{Based  on  British  Freeboard  Tables.) 

It  is  often  necessary  to  get  an  approximation  to  the  load  draught 
in  estimating  on  proposed  vessels,  when  in  many  cases  there  is 
insufficient  time  to  calculate  the  freeboard  in  the  regular  way. 
For  this  purpose  the  adjoining  diagrams  have  been  prepared  for 
cargo  vessels  from  the  freeboard  tables,  and  from  these  the  mean 
moulded  load  draught  may  be  scaled  off  with  accuracy,  always 
observing  that  the  proper  allowances  for  excess  of  sheer,  erec- 
tions on  deck,  and  uncovered  iron  deck,  strength,  etc.,  must  be 
made  afterwards.  These  diagrams  being  graphic  reproductions 
of  the  various  tables,  will  be  found  to  facilitate  the  estimating  of 
load  draughts  where  a  sufficiently  close  approximation  only  is  re- 
quired. It  should  also  be  borne  in  mind  that  fullness  of  form 
influences  the  freeboard  to  a  considerable  extent,  therefore  the 
diagram  will  only  read  correctly  for  vessels  having  coefficients  of 
under  deck  tonnage  from  .78  to  .82,  and  judgment  must  be  used 
when  dealing  with  vessels  of  finer  forms,  the  freeboards  of  which 
are  less  than  in  the  case  of  fuller  vessels. 


Load   Draught  Diagrams 


91 


uvaa  avon  Nvaw  aaonnow  jo  3ivqs 


92 


The   Naval   Constructor 


DIAGRAM  SHOWING  RELATIVE  DEPTHS  AND  LOAD 
DRAFTS  IN  VARIOUS  TYPES  OF  VESSELS. 

PROPORTIONS (5-)  IN  SPAR  DECK  SHIP  TAKEN  TO  SPAR  DECK(7'-o"  ABOVE  MAIN  DEC! 

"               "    "AWNING     "        "          "         "    MAIN       " 

"               "    "SAILING                "          "        "UPPER      " 
D     DEPTH   MOULDED  TO   RESPECTIVE    DECKS. 

c) 

\ 

0  ,, 

NOTE:- -ALLOWANCES  FOR  EXCESS  OF  SHEER  AND                                         \,  e£- 

M^g 

?$>' 

26' 

,\&  $• 

i^wr? 

..  >1 

&&* 

^ 

24/ 

FOR  GIVEN  DEPTH. 

Jjf> 

e* 

Kfr 

V 

#\' 

22'    ^ 

2«V 

5> 

"\C 

u. 

"^ 

^C^ 

& 

&*. 

20'  g 

^ 

^ 

j^5" 

K\V 

O 

'i4& 

JV> 

ttf 

18'   § 

k 

C 

>^> 

-1 

y^\     ( 

16'   % 

s^T  .0 

a& 

w 

B* 

r 

1*'    Q 

y 

^ 

s^/ 

111 

s* 

# 

12'    3 

i£ 

& 

3 
O 

s 

^ 

"7* 

10'    = 

U^ 

«§' 

L. 
O 

r^ 

y 

8  '     u 

p 

_i 

< 

* 

6'     ° 

D           CD 

00 

0 

OJ 

■* 

CO 

CO 

(V 

CM 
C\J 

s 
CM 

to 

CM 

00 

O 
CO 

CJ 

CO 

.MOULDED  DEPTH, TO  MAIN  DECK    IN  SPAR  AND  AWNING  DECK  VESSELS 
"               •"          "UPPER    "       ««    SAILING  SHIPS. 

JFlG.  32. 


Kirk's  Analysis  93 


CHAPTER   V. 

KIRK'S    ANALYSIS. 
(Trans.  Inst,  of  Nam.  Arch.) 

The  following  was  the  method  adopted,  and  here  I  may  premise 
that  for  ordinary  purposes  I  assumed  that  the  length  of  entrance 
and  rim  were  equal  —  in  fact  I  contented  myself  by  finding  the 
mean  of  the  lengths  and  angles  of  entrance  and  run  —  but  the 
method  is  equally  applicable  to  finding  them  separately  when 
greater  accuracy  is  required. 

I  shall  now  give  the  process  for  finding  the  mean  length  and 
angle  of  entrance  and  run. 

Construct  a  block  ship  having  the  same  displacement,  mean 
draught,  and  area  of  midship  section  as  the  ship  under  considera- 
tion, but  with  rectangular  sections,  parallel  middle  body  (if  neces- 
sary) and  straight-sided  wedge-shaped  ends.  Fig.  3$  shows  by  the 
curved  line  IBK  the  midship  section  of  the  actual  ship,  and  by  the 
rectangle  CLME  the  midship  section  of  the  block  ship,  both  sec- 
tions being  equal  in  area  and  depth,  having  a  common  water  line 
IK.  The  depth  AB  is  the  mean  draught  of  the  ship.  Fig.  ■'.'> 
represents  the  block  ship,  and  ABDC  is  the  half-breadth  plan, 
the  sides  being  vertical,  the  transverse  sections  all  rectangular,  and 
the  keel  parallel  to  the  water  line.  The  sides  CD  and  EF  which 
form  the  middle  body,  are  parallel  to  the  keel  (or  to  the  centre 
line  AB),  and  the  half-breadth  GC  or  HD  is  equal  to  AC,  Fig. 
3^  34,  the  half-breadth  of  the  equivalent  rectangular  midship  section 
(which  is  in  fact  the  midship  section  of  the  block  ship),  EL  being 
also  equal  to  AB.  The  angles  CA  G  and  DBH  are  equal,  and  while 
the  length  AB  is  equal  to  the  length  of  the  ship,  the  length  AG  or 
HB  of  equal  wedges  which  form  the  ends  is  such  that  the  area  of 
the  figure  ACDBFE  multiplied  by  the  mean  depth  AB,  is  equal 
to  the  volume  of  the  displacement  of  the  actual  ship. 

Complete  the  rectangle  COPE  as  in  the  dotted  lines.  It  is 
obvious  that  the  rectangular  solid  COPELQ  is  equal  in  volume  to 
that  of  the  block  ship,  in  fact  to  the  volume  of  the  displacement  of 
the  actual  ship,  and  that  the  length 

~„.     ,  Displacement  in  cubic  feet 

GB  in  feet  =       .    l   , , 

A iea  ot  midship  section  in  square  feet 

and  the  mean  length  of  entrance  and  run 

.  r,      ,       ..      ,    ,.        Displacement 

A G  =  length  of  ship—  -7—£-—. —■> 

Midship  area 


94 


The   Naval   Constructor 


|Zi 

8 

hi 

Ph 
O 
« 

2£ 
H  O 

Oh 

H 

u 

EC 

m 
o 

M 

o 

« 

05 
02 

o 

« 

Principal 
Dimensions. 

Draught 
of  Water 
Trial. 

l 

9N 

Displace- 
ment. 

Midship 
Section. 

0)  b-  S 
h3£  g 

.d-d 

a;  2 

^  o 

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u 

o 

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< 

3D 

a 
o 
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d 

C  * 

(J)  rH 
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<»  £ 

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E.S 

°^ 

/    // 

/   // 

/  '/ 

i   n 

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1 

s.s. 

2,811 

342  0 

38  0 

29  11 

18  6 

20    2 

19 

4 

4,500 

.658 

643 

.92 

2 

s.s. 

2,811 

342  0 

38  0 

29  11 

18  4 

19    9 

19 

0£ 

4,415 

.656 

630 

.916 

3 

s.s. 

2,911 

344  0 

39  0 

29  11 

16  0 

20    0 

18 

0 

4,235 

.647 

604 

.907 

4 

s.s. 

2,965 

348  0 

39  0 

29  11 

17  3 

19  11 

18 

7 

4,472 

.653 

626 

.91 

5 

s.s. 

974 

230  0 

32  0 

19    0 

7  0 

13    0 

10 

0 

1,227 

.625 

266 

.89 

6 

s.s. 

979 

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32  0 

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14  9 

14  11 

14 

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2,034 

.683 

423 

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s.s. 

1,158 

240  0 

32  0 

19  11 

11  7 

13    8 

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7i 

1,693 

.647 

344 

.902 

8 

s.s. 

2,014 

285  0 

35  0 

26    6 

13  7 

15  10 

14 

8£ 

2,710 

.685 

454 

.936 

9 

s.s. 

534 

190  0 

25  6 

15    0 

11  7 

12  11 

12 

3 

1,115 

.694 

268 

.904 

10 

T.S 

280  0 

60  0 

42    6 

24  3 

25    3 

24 

9 

7,555 

.663 

1,287 

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11 

p. 

.  .  . 

203  8 

26  6 

16    0 

10  6 

10    6 

10 

6 

885 

.581 

230 

.87 

12 

30  0 

22    6 

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12 

8 

1,235 

.533 

285 

.79 

13 

p. 

•     •     • 

98  0 

18  0 

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4  9 

5    3 

5 

0 

133 

.575 

785 

.87 

14 

s.s. 

2,160 

320  0 

40  0 

21    8 
to  main 

8  9 

17    4A 

13 

Of 

2,335 

.522 

387 

.791 

deck. 

Kirk's  Analysis 


11.-, 


- 
- 

A  ^^ 

C 

D 

2   3 

CO      1 

'■w        JH 

MODE 

L 

|1 

£> 

jG 

SO 

J.      ■ 

E    • 

F 

-i"c 

I.II.P. 

Speed  in  k.noi 

*  - 

—  < 
■-  'i 

i- 
|» 

a 
< 

Immersed  Surfa 

Divided  by 

mersed  Surface 

3     Length  A. B. 

w 
6 

c2 
9 

■~ 

pq 

Draught  For- 
ward and  Aft. 

Length 

of  Entrance 

A.(i. 

O 

3d 

s 

Half  Angles 

of  Entrance 

V.AM. 

Area 
of  1  mmersed 

Surface. 

Sq.  Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

o     / 

Sq.  Ft. 

1,431 

11.52 

19,348 

329.5 

34.8 

18.5 

84.6 

86.4 

11  38 

20,847 

.928 

642 

9.18 

19,140 

329.5 

34.6 

18.2 

84.2 

85.9 

11  37 

20,605 

.929 

1,429 

11.87 

18,892 

331.5 

35.3 

17.1 

86.1 

87  9 

11  35 

20,123 

.938 

2,106 

12.94 

19,506 

335.5 

35.4 

17.7 

*.-...-. 

S7.3 

11  42 

20,854 

.935 

528 

9.32 

8,552 

223.2 

28.3 

9.4 

61.8 

63.4 

12  54 

8,824 

.969 

805 

10.33 

10,850 

223.2 

29.8 

14.2 

54.9 

56.9 

15  11 

11,468 

.946 

909 

11.14 

10,216 

232.5 

28.7 

12.0 

60.3 

62.0 

13  23 

10,604 

.963 

1,195 

11.57 

13,947 

277.7 

32.4 

14.0 

68.8 

70.7 

13  15 

14,650 

.952 

441 

8.63 

7,300 

184.5 

22  :» 

11.7 

38.9 

40.5 

16  24 

7,726 

.945 

.  .  . 

.  .  . 

24,021 

283.0 

54.1 

23.8 

TT.r. 

82.1 

19  14 

25,026 

.96 

1,135 

13.33 

6,700 

203.0 

23.2 

9.9 

68.3 

69.3 

9  38 

7,185 

.932 

1,450 

12.66 

8,440 

220.8 

23.7 

12.0 

69.1 

70.1 

9  44 

8,942 

.944 

125 

8.54 

1,935 

97.5 

15.5 

4.0 

32.4 

33.3 

13  27 

1,922 

.993 

2^252 

13.89 

13,750 

312.0 

31.5 

12.3 

100.8 

102.0 

8  53 

14,387 

.955 

96 


The   Naval   Constructor 


also, '  The  breadth  CE  =   Area  midshiP  section 


>i 


<D 


r21 


\-  \\7.7 


I 


H6.5- 


r,7- 


Mean  draught  (ex.  keel) 
and  the  tangent  of  the  mean  half- 
angle  of  entrance  and  run, 

CAG  =  <£. 

Thus  from  the  length,  breadth, 
draught,  area  of  midship  section, 
and  displacement,  the  mean 
length  of  entrance  and  run  and 
the  mean  angle  can  be  got.  There 
are  other  methods  of  working  this 
out,  which  will  occur  to  any  one, 
but  the  method  given  is  perhaps 
the  simplest. 

In  order  to  get  the  length  and 
angle  of  entrance  and  run  sepa- 
rately (instead   of  the    mean   as 
stated),  it  is  necessary  to  have  in 
addition,  the  displacement  in  two 
portions,  one  forward  of  the  mid- 
ship section,  and  one  aft,  the  dis- 
tance  of  the  midship  section  from    «p 
one  end  of  the  ship,  and  the  mean     w 
draught  of  each  of  these  portions ;     ^ 
treating  them,    in  fact,    as   two 
separate  ships,  one  of  which  has 
no  run  and  one  no  entrance. 

In  my  earlier  attempts  I  re- 
tained the  actual  breadth  of  the 
ship  as  the  breadth  of  the  block 
ship,  and  varied  the  depth,  but 
I  prefer  the  plan  before  given  of 
using  for  the  block  ship  the  mean 
draught  of  the  actual  ship.  In 
ships  with  extremely  raking 
sterns  or  stern  posts,  I  take  the 
length  at  half  depth  when  that 
can  be  got  (or  the  mean  length) 
as  the  length  of  the  block  ship. 
In  single  screw  steamers,  I  take 
the  length  to  the  forward  stern 
post. 

The  block  ship  will  often  be 
found  of  use  in  forming  first  or 


►K 


?l> 


l" 


7.  7H 


H7.S- 


|-17.0- 


rf  +•  8-^ 


/7.9 


■J) 


to 


O 


Wetted  Surface  97 

approximate  designs,  and  in  this  view  it  may  be  interesting  to 
compare  the  wetted  skin  surface  of  actual  ships  with  that  of  the 
equivalent  block  ships,  this  being  an  important  element  in  speed 
calculations  and  otherwi.se. 

In  the  foregoing  table  I  have  selected  fourteen  ships  of  very- 
diverse  types,  giving  their  dimensions,  block  models,  actual 
wetted  surface  (exclusive  of  that  of  keels  or  rudder),  and  wetted 
surface  of  block  ship,  and  the  ratio  of  one  to  the  other. 

From  this  it  will  be  seen  that  in  iirst  approximations  in  compar- 
ing one  ship  with  another  we  shall  not  commit  a  grievous  error 
in  using  the  surface  of  the  block  ship,  and  also  that  a  very  close 
approximation  indeed  may  be  made  to  the  actual  wetted  surface 
by  multiplying  the  surface  of  the  block  ship  by  one  of  the  coeffi- 
cients in  the  table,  according  to  the  type  of  the  ship.  In  the 
second  column  SS  means  single  screw,  TS  means  twin  screw,  and 
P  paddle.  In  No.  10  I  ought  to  explain,  that  not  only  was  the 
rudder  of  exceptional  breadth,  part  of  which,  to  make  the  com- 
parison with  the  others  more  even,  has  been  included,  but  there 
was  a  peculiar  overhanging  portion  under  water  near  the  top  of 
the  stern  post,  by  which  the  mean  length  taken  for  the  block  ship 
exceeds  that  of  the  actual  ship  between  perpendiculars. 

To  show  more  clearly  the  relation  of  the  block  model  to  that  of 
the  actual  ship,  I  have  selected  No.  4  in  the  table,  as  being  a  fair 
example  of  a  merchant  mail  steamer  of  considerable  speed,  and  in 
Fkr.  30  I  have  siven  the  curve  of  areas  of  transverse  sections ;  and 
I  have  put  it  in  this  form  that  the  ordinates  are  equal  to  the  half 
areas  of  the  corresponding  transverse  sections  divided  by  the 
draught  of  water  (less  depth  of  keel)  at  the  several  sections. 
Thislsin  fact  the  curve  of  form,  or  fineness  of  model. 

Above  this  I  have  drawn  the  half-breadth  plan  of  the  block 
ship,  the  length,  breadth,  and  area  of  this  being  of  course  equal  to 
those  of  the  curve,  and  the  length  and  angle  of  entrance  and  run 
a  mean  of  those  of  the  actual  curve  of  form. 

Wetted  Surface  Formula. 
W.S.=X  >'  (P'  +dr)xc. 


(!+*) 


Where  W.S.  =  wetted  surface  of  hull  proper  in  square  feet,  ex- 
cluding bossing,  rudder,  bar  keel,  etc. 

L  =  length  on  load  water  line. 

B  =  extreme  breadth. 

dr  =  extreme  draught  in  flat  plate  keel  vessels,  and 
draught  corrected  to  flat  plate  keel  conditions  in 
bar  keel  vessels. 

c  =  constant  from  the  following  table  : 


98 


The  Naval  Constructor 


Ratio  of 

#  =5.00 
dr 

3.33 

2.50 

2.00 

1.667 

Block  Co- 
efficient. 

-c 

-\ 

ralues  of  "c 

»9 

— >- 

.40 

1.120 

1.130 

1.153 

1.180 

1.200 

.45 

1.167 

1.184 

1.211 

1.240 

1.260 

.50 

1.215 

1.238 

1.270 

1.300 

1.320 

.55 

1.272 

1.299 

1.330 

1.360 

1.380 

.60 

1.330 

1.360 

1.390 

1.420 

1.440 

.65 

1.397 

1.427 

1.456 

1.480 

1.500 

.70 

1.465 

1.494 

1.522 

1.541 

1.560 

.75 

1.542 

1.565 

1.588 

1.604 

1.620 

.80 

1.620 

1.637 

1.655 

1.668 

1.680 

.85 

1.708 

1.715 

1.724 

1.733 

1.740 

Wetted  Surface  (Taylor's  Formula). 

W.S.  =  c  \/Dx  L. 

where  W.S.  =  wetted  surface  in  square  feet,  excluding  rudder, 

bossing,  etc.: 
D  =  displacement  in  tons  of  35  cubic  feet. 
L  =  mean  immersed  length. 
B  =  breadth  extreme. 
H  =  draught  of  water,  extreme  in  flat  plate  keel  vessels, 

and  corrected  to  flat  plate  keel  conditions  in  bar 

keel  vessels, 
c  =  constant  found  from  the  following  table  : 


T> 

Ratio  ■=« 

XX 

Constant  "c." 

Ratio  -—  • 

xi 

Constant  "c." 

2.0 

15.63 

2.8 

15.55 

2.1 

15.58 

2.9 

15.58 

2.2 

15.54 

3.0 

15.62 

2.3 

15.51 

3.1 

15.66 

2.4 

15.50 

3.2 

15.71 

2.5 

15.50 

3.3 

15.77 

2.6 

15.51 

3.4 

15.83 

2.7 

15.53 

3.5 

15.89 

Note.  —  This  formula  becomes  unreliable  when  the  block  coefficient  is 
beyond  the  limits  of  .45  and  .75,  or  when  the  ratio  of  —  is  outside  the  limits 

XX 

given  in  the  table. 


.aunchin< 


99 


CHAPTER   VI. 
LAUNCHING* 

The  form  of  ways  for  ordinary  merchant  ships  is  of  compara- 
tively little  importance  ;  but  in  special  cases,  such  as  armored  war 
vessels  or  long,  light  river  boats,  if  there  is  too  little  water  on  the 
way  ends,  the  vessel  is  liable  to  tilt  as  soon  as  her  C.G.  gets  over 
the  way  ends,  and  being  as  it  were  pivoted  at  this  point,  a  great 
pressure  is  put  upon  the  bottom  of  the  vessel,  causing  undue  local 
strains,  which  might  possibly  force  in  the  bottom  plating,  frames, 
etc.,  in  those  vessels  which  are  not  so  strongly  constructed  as  ordi- 
nary merchant  vessels,  or  the  ways  might  collapse  here  and  then 

1-     COMMENCEMENT   OF  1st  PERIOD 

2.    CHANGE  BETWEEN  1ST  &  2N0  PERIODS 

3-     END  OF2"o  PERIOD 


267  250     210  200 

Fio.  36. 


ICO 


the  vessel  would  be  left  to  slide  off  the  remaining  distance  on  her 
keel.  To  guard  against  this  danger,  it  is  desirable  to  ascertain  by 
calculations  and  diagrams  if  the  form  of  the  ways  is  such  that  the 
vessel  may  be  launched  without  fear  of  tilting. 

The  time  that  a  vessel  takes  to  travel  down  the  ways  may  be 
divided  into  two  periods  —  the  first  lasts  while  she  rests  entirely 

•  Paper  by  H.  G.  Gannaway,  Trans.  K.  Coast,  Eng.,  and  Shipb'd,  1887. 


100  The   Naval   Constructor 


on  the  ways,  and  the  second,  when  the  stern  is  afloat  and  the  fore 
end  of  the  ship  is  bearing  on  the  fore  end  of  the  sliding  ways. 

A  base  line  is  first  drawn,  the  measurements  along  which  repre- 
sent distances  travelled  by  the  ship  down  the  ways,  the  total 
length  in  this  case  being  267  feet.  The  line  AA  drawn  parallel 
to  the  base  represents  the  moment  of  the  ship  about  the  fore 
end  of  the  sliding  ways.  In  this  example  the  ship's  weight  is 
865  tons,  which  being  multiplied  by  97.2  feet,  the  distance  of  the 
C.G.  of  the  ship  from  the  fore  end  of  the  sliding  ways,  =84,121 
foot-tons.  The  buoyancy  moments  about  the  same  point  are  rep- 
resented by  curve  B.  The  position  of  intersection  of  this  curve 
with  the  line  A  A  will  indicate  where  the  vessel  will  be  when  her 
stern  commences  to  float  aft.  At  this  point  the  first  period  ends 
and  the  second  commences,  which  in  the  example  is  when  the 
vessel  has  travelled  208'  6"  down  the  ways.  Although  this  is  the 
point  where  the  moments  of  buoyancy  and  weight  about  the  fore 
end  of  sliding  ways  become  equal,  the  vessel's  stern  does  not 
actually  lift  until  she  has  moved  a  few  feet  beyond  this,  because 
an  additional  amount  of  displacement  is  required  to  overcome  the 
vertical  component  of  the  ship's  momentum. 

Observations  of  the  dip  of  the  vessel's  keel  have  proved  that 
this  additional  displacement  is  so  trifling  that  a  complete  investi- 
gation of  its  amount  is  unnecessary  for  ordinary  purposes. 

The  displacement  of  the  vessel  throughout  the  first  period  is 
shown  by  curve  D1,  and  for  the  second  period  by  curve  D2.  Dur- 
ing the  second  period,  the  after  end  of  the  vessel  being  afloat,  and 
the  fore  end  resting  on  the  sliding  ways,  it  is  evident  that  the 
buoyancy  moment  about  that  point  will  remain  the  same  as  the 
weight  moment  all  throughout  this  period.  The  displacement,  of 
course,  increases  as  the  vessel  moves  down  the  ways,  but  the 
gradual  lifting  of  the  stern  and  lowering  of  the  bows  brings  the 
C.B.  further  forward,  and  so  reduces  the  leverage  while  the  dis- 
placement is  increasing,  thus  retaining  practically  a  constant  mo- 
ment. The  distance  that  the  line  CC  is  above  the  base,  represents 
the  weight  of  the  ship,  the  weight  on  the  fore  end  of  the  sliding 
ways  being  proportional  to  the  distance  between  this  line  and 
curve  of  displacement  D2.  This  weight  is  225  tons  at  the  begin- 
ning of  the  period,  and  is  reduced  to  115  tons  at  the  end.  It  is 
important,  therefore,  that  the  fore  end  of  the  cradle  should  be 
made  sufficiently  strong  to  carry  the  load  which  is  thus  put  upon 
it.  It  will  be  seen  then  that  it  is  desirable  to  reduce  the  duration 
of  the  second  period  as  much  as  practicable,  for,  since  the  longer 
it  is,  the  greater  the  weight  will  be  on  the  fore  end  of  the  sliding 
ways,  which  in  the  case  of  heavy  vessels  renders  them  liable  to 
come  down  to  the  ground  and  damage  their  fore  ends. 

In  considering  the  subject  of  tipping,  we   take   the   moments 


Launching 


H)l 


about  the  end  of  the  standing  ways,  and  ae  lcn£  ae  'he  badyaricy 
moment  remains  in  excess  of  the  weight  moment  about  this  point, 
there  is  no  fear  of  the  vessel  tipping;  but  if  in  any  position  the 
former  moment  falls  short  of  the  latter,  it  is  evident  that  in  order 
to  restore  equilibrium,  the  stern  will  drop,  and  thus  increase  the 
displacement  until  both  moments  are  equal.  Tipping,  if  occurring 
at  all,  must  take  place  after  the  C.G.  of  the  ship  has  passed  the 
end  of  the  standing  ways,  and  before  the  commencement  of  the 
second  period.     In  the  example,  the  C.G.  of  the  ship  has  passed 


;cales 

^"^^-1                   A 

B 

f!tons 

E 
FlTONS 

D 

TONS. 

80,000 

16,000 

800 

\ 

■^D 

_ 

10,000 

2,000 

100 

40  OVER 


30  20 

Fig.  37. 


10 


(|>AT  WAY  END8 


the  way  ends  when  she  has  moved  174  feet.  From  about  that 
point  to  a  little  beyond  the  end  of  the  first  period,  the  buoyancy 
and  weight  moments  about  the  end  of  the  standing  ways  are  cal- 
culated at  several  intervals,  and  at  each  interval  the  latter  moment, 
being  deducted  from  the  former,  gives  the  moments  against  tip- 
ping. These  moments  are  shown  by  curve  E.  If  this  curve  at 
any  part  were  to  run  below  the  base  line,  it  would  show  that  the 
vessel  will  tilt.  The  point  where  this  curve  is  nearest  to  the  base 
line  gives  the  position  of  the  vessel  when  she  has  least  longitudi- 
nal stability,  which  in  this  case  is  when  the  vessel  has  travelled 
down  the  ways  189  feet,  the  minimum  margin  against  tipping  be- 
ing 9,700  foot-tons. 

It  is  desirable  that  the  margin  be  not  too  small  for  uncertain 
ssels;  where  this  was  the  case  they  actually  did  tilt  slightly, 
which  shows  that  a  moderate  margin  is  required  in  calculation  to 
allow  for  the  error  introduced  by  treating,  as  it  is  convenient  to 
do  in  practice,  those  moments  statically  instead  of  dynamically. 
In  calculating  the  buoyancy  moments  no  account  is  taken  of  the 
cradle,  which  would  only  alter  the  results  slightly  ;  the  variations 
being  on  the  right  side,  may  be  safely  ignored.     Besides,  the  after 


102 


The   Naval   Constructor 


Table  of 


INDEX    LETTER. 


Description 
of  Vessel  and  Moulded  Dimen- 
sions in  Feet. 


Length 


Declivity  of  keel  per  foot  . 
Declivity  of  standing  ways  per 

foot 

Camber  of  standing  ways  .     . 
of    standing    (  Inner 

ways (  Outer 

Length      of      sliding    j  Inner 

ways I  Outer 

Breadth     of     sliding    (  Inner 

ways (  Outer 

Area  of  sliding  ways  in  square 

feet 

Total  fall  in  length  of  standing- 


ways  

Water  on  way  ends  .     .     . 
Draught  of  ship  forward    . 
Draught  of  ship  aft  .     .     . 
Draught  of  ship  mean  . 
Displacement  in  tons     . 
Mean  pressure  per  square  foot 

on  sliding  ways  in  tons  . 
Length  of  first  period    . 
Length  of  second  period    . 
Ratio  of  length  of  2d  period  to 

length  of  sliding  ways    . 
Weight  on  sliding  ways  at  com 

mencement  of  2d  period 
Weight  on  sliding  ways  at  end 

of  second  period  (in  tons) 
Margin  against  tipping  . 


pro 

^  x 

.  © 

HC0 


1  G 


_8_  +n  I8 

T6    LU    1  0 

2' 3" 

345' 

288' 

240' 

105' 

V  10" 

V  8" 

1,430 

23'  0" 
8' 7" 

ir2" 

16' 6" 

13'  10" 
2,850 

2.00 

278.0 
67 

28% 

520 

250 
10,500 


H  so 
02 


_8_" 
1  6 


jl  to  i| 

ro" 

J367' 

'  284' 


1'9' 


994 

18'  9" 

CO" 
11'  6" 
14'  0" 
12'  9" 

2,500 

2.51 

283 
84 

30% 

550 

290 
33,250 


c 


(i.  "Id 

*?> 

oi  <# 

£X 

So 

r  © 


16 


8      fo  I1 
16    to  T6 

1'2" 


°95' 


o 


330' 


1'9' 


1,155 
19'  7" 

7'0" 

10'  10i 
9' Of" 
2,157 

1.9 

250.5 
144.5 

44% 

640 

300 
80,000 


D 


£X 

02 


8   // 

IS" 


8     tnll 

re  LO  T 6 

ro" 

370' 
305' 

i'9,; 

1,067 

18'  6" 
2' 6" 

8' Of 
10'  5" 

9'  21" 
2,240 

2.09 

279.5 

90.5 

30% 

630 

380 
35,300 


Table   of   Launching   Data 


103 


Launching  Data. 


E 

i 

(; 

ii 

J 

K 

I- 

M 

•.    — :i 

: 

J.  ■■: 

£  — 
-  x 

J^  1-1 

: 

EC  S 

—  ri 

KX 

-  3 

•  ■- 

: 

- 
bd » 

-  ■-. 

-  :< 

- 

5 
-  ?. 

r:  ^ 

-  X 

•   ?\ 

J. 

^x 

si 

oo 

—  -T 

CO 

-  * 

< 

-x 

'-  ti 

3D 

-  a 
3D 

9  // 

9   // 
19 

8   It 
IS 

a  // 

T6" 

8  // 
l  S 

8   W 

16 

_s_  to  J4 

16    LU    1  6 
I'll" 

8     fn  1  6 
lZ  l°  T6 

l'lO" 

_iL  to  i| 
1 S   LU  1  6 

1'  10" 

_3_  to  ii 
16    LU    10 

l'O" 

re  lo  to 
10" 

10    fn    14 

tj  lo  re 

8" 

l'O" 

_9     tO  i3 

6" 

348' 

302' 

300' 

267' 

250' 

195' 

259* 

276' 

240' 

200' 

200' 

180' 

170' 

150' 

207' 

100' 

no- 

1'8" 

1''.' 

1".'" 

1'9" 

1'3" 

l".i" 

l'O" 

880 

660 

700 

630 

595 

375 

7  2  5 

665 

21' 6" 

18' 10- 

17  6" 

15' 4" 

14' 6" 

12'  0" 

15'  0" 

10' it" 

3' 9" 

3'1<»" 

3' 7" 

2'  8" 

4' 5" 

2'  '.»" 

1' «.)'' 

2'0" 

0'  6  V 

6'  0" 

5' 7" 

5' 9" 

8' 7" 

4,0,/ 

6' 11" 

9' 2" 

9' 5  4" 

8' 2" 

10'  8" 

9'0" 

7'1" 

3'  10" 

9'  11" 

12'  0" 

8'  ("»" 

7'1" 

8'iy 

7' 41" 

7'  10" 

3'  11" 

8' 5" 

10'  7" 

1,600 

1,100 

1,000 

865 

700 

215 

1,015 

1.750 

1.89 

1.65 

1.40 

1.37 

1.16 

..".7 

1.4 

2.63 

237.5 

202 

249 

2(»8.5 

190 

122 

l'Il' 

110.5 

100 

51 

58.5 

60 

—  -i 

I  6 

47 

.  .  . 

4.; 

50% 

25i% 

32  i% 

35% 

49% 

23% 

.  .  . 

560 

400 

215 

225 

225 

235 

.  .  . 

255 

125 

110 

115 

115 

25 

170 

63,600 

39,000 

6,400 

9,700 

12,300 

5,500 

.  .  . 

.   .  . 

104  The  Naval  Constructor 

end  of  the  sliding  ways  often  rises  to  the  surface  shortly  after  the 
vessel  has  entered  the  water.  In  the  diagram  a  complete  set  of 
curves  has  been  given  to  fully  illustrate  the  matter,  but  for  prac- 
tical purposes  only  that  part  of  the  diagram  where  the  vessel  is 
represented  to  be  moving  from  the  position  where  the  C.G.  is  at 
the  way  ends,  to  the  end  of  the  second  period,  is  required. 

As  the  minimum  moment  against  tipping  is  a  very  important 
thing,  it  will  be  useful  to  know  what  variation  will  be  made  in  its 
amount  by  any  alteration  to  the  length  and  form  of  the  standing 
ways  of  this  vessel : 

Lengthening  the  standing  ways  10  feet  increases  the  moment 
from  9,700  to  13,700  foot-tons. 

Shortening  the  ways  10  feet  decreases  the  moment  to  5,300  foot- 
tons. 

Increasing  the  camber  from  12  inches  to  18  inches  increases  the 
moment  to  14.500  foot-tons. 

Decreasing  the  camber  to  6  inches  decreases  the  moment  to  4,000 
foot-tons. 

If  with  a  certain  declivity  of  ways  for  the  launching  of  a  vessel, 
it  is  found,  by  calculation,  she  will  tilt,  the  standing  ways  must  be 
extended  further  out  into  the  water,  or,  if  this  cannot  be  done 
conveniently,  their  outer  ends  must  be  lowered,  or  ballast  put  into 
the  fore  end  of  the  vessel.  The  first  two  increase  the  buoyancy 
moment  about  the  end  of  the  standing  ways,  and  the  third 
decreases  the  weight  moment  about  the  same  point. 

W  sin  5  -fW  cos  8 
Pressure  on  dog  shores  = fl 

~W  =  weight  of  vessel. 

5  =  mean  angle  of  declivity  of  ways  under  vessel. 
j8  =  angle  between  ways  and  dog  shores. 
/  =  coefficient  of  friction  (between  1.0  and  .7). 

The  ratio  of  second  period  to  length  of  sliding  ways  cannot  be 
got  lower  than  about  25  per  cent  without  danger  of  tipping. 


Rudders 


105 


RUDDERS. 

In  determining  the  most  suitable  area  of  rudder  it  is  usual  to  take 
the  same  as  a  percentage  of  the  immersed  longitudinal  plane  of 
the  ship,  which  percentage  will  vary  with  the  degree  of  fineness 
of  the  vessel. 

Percentage  for  Rudder  Area  in  Various  Types. 


Type  of  Vessel. 

Per  Cknt  of 

Immersed  Lokgi- 

Tri)i.\AL  Plank. 

1.25 

1.50 
1.10 
2.0 

Having  fixed  upon  the  area,  the  diameter  of  stock  may  be 
calculated  by  various  formulas,  some  of  them,  unfortunately,  of  a 
very  approximate  character,  and  on  this  account,  where  high 
speed  will  be  attained,  it  is  advisable  to  carefully  calculate  the 
required  diameter  irrespective  of  the  result  obtained  by  the  classi- 
fication societies'  formula?.  For  this  purpose  it  is  necessary  to 
kimw,  (1)  the  hard  over  angle  of  rudder,  (2)  centre  of  pressure  on 
rudder  blade,  (3)  maximum  pressure  exerted  at  hard  over  with 
ship  at  full  speed.  The  angle  of  helm  being  usually  35°,  the 
pressure  on  blade  at  this  angle  at  full  speed  may  be  found  from 
the  formula,  — P  representing  the  pressure  in  lbs. 

P  =  AV'2X  sin  aXp. 

It  should  be  stated  that  F=  speed  of  vessel  in  knots  per  hour 
plus  20  per  cent  to  allow  for  the  slip;  .l=area  of  rudder  in 
square  feet,  including  emerged  surface;  and  p  =  pressure  in  lbs. 
per  sq.  foot  at  1  knot,  =3.19  lbs.  per  sq.  foot. 

Before,  however,  the  twisting  moment  on  the  stock  can  be 
solved,  the  centre  of  pressure  must  be  located.  This  centre  bei  s> 
4;  the  breadth  from  the  leading  edge  with  the  helm  amidships,  does 
not  arrive  at  the  centre  of  gravity  of  rudder  until  90°  is  reached, 
and  as  35°  is  the  usual  anele,  it  will  be  sufficiently  close  to  take  .37 
of  the  breadth  of  the  rectangle  equalling  the  rudder  area  : 

Centre  of  pressure  from  centre  of  stock  =  1=  V  .-°>7. 


106 


The   Naval   Constructor 


The  twisting  moment  T  would  then  be 

T=  A  V2  X  sin  35°  x  3.10  x  I  =  inch-pounds, 

and  equivalent  diameter  of  stock  "d  "  in  inches  with  a  fibre  stress 
k  of  5,000  lbs., 

3/  jr- 

The  subjoined  table  gives  torsional  moments  with  their  equiva- 
lent diameters  calculated  as  above,  with  *  5,000  lbs.  per  square 
inch,  being  a  sufficiently  high  fibre  stress  to  allow  for  a  twisting 
stress,  alternating  between  right  and  left,  for  wrought  iron. 

In  a  rudder  of  rectangular  form  the  centre  of  pressure  from  the 
leading  edge  is  equal  to 

b  (.  195  +  .305  sin  a)  =  5c, 

where  b  is  the  mean  breadth  of  rudder,  and  c  a  coefficient,  as  under. 


Angle  of 
Rudder,  a. 

c. 

AXGLE  OF 
KUDDER,  a. 

c. 

10° 
20° 
30° 

.248 
.300 
.347 

35° 
40° 
45° 

.370 
.301 
.410 

Rudder  Stocks  per  Lloyd's  Rule. 

The  following  is  the  formula  prescribed  by  Lloyd's  Register  for 
estimating  diameters  of  rudder  stocks,  but  in  no  case  must  the 
result  be  less  than  the  tabulated  rule  size,  which  see.  It  should 
not,  however,  be  used  unless  the  ship  is  intended  for  classification 
in  that  society's  register,  as  for  very  high  speed  vessels  the 
results  obtained  would  be  too  weak.  One  of  the  factors  is  draught 
of  water,  which  has  little  or  no  value  in  computing  the  strength 
of  rudder  stock  for  a  rudder  of  ordinary  type  hung  on  a  post.  Of 
course,  in  a  rudder  with  no  bottom  bearing,  as  in  destroyers  and 
such  craft,  the  case  would  be  entirely  different,  as  then  the  stock 
would  be  figured  for  bending,  the  moment  for  such  being  much  in 
excess  of  the  torsional  one. 

*  Take  7,000  lbs  for  steel. 


Rudder  Stock   Diameters 


107 


Rudder  Stock  Diameters. 


TORSH.N   \  |. 

PlAM  1- 

TORSIONAL 

T  >  I  LM  K- 

Tobsiob  \  I. 

Di  \  m  i:- 

Moment 

TKK  OK 

MOMENT 

TKIi  OP 

-M<>m  in  r 

TKIt    OF 

"jT"   IX 

Sti«  k 

"  7'"  ix 

Sto<  k 

uTn   IN 

Stock 

LNCH-LBS. 

in  Ins. 

1  N<  H-LBS. 

IN    [NS . 

Inch-lbs. 

IN  Ins. 

20,000 

2| 

500,000 

8 

3,260,000 

1") 

2.">,000 

3 

550,000 

»i 

:;..-,oo,ooo 

15f 

50,000 

3| 

000,000 

H 

3,750,000 

15f 

75,000 

H 

650,000 

8| 

■1.01 10.  in  m 

16 

100.000 

4| 

700,000 

9 

4,250,000 

16J 

120.000 

5 

800,000 

Q  1 

B 

4,500,000 

m 

140,000 

H 

900,000 

•  t 

4.750,000 

17 

1  HO,  000 

H 

1.(100,000 

10 

5,000,000 

m 

180,000 

5| 

1,200,000 

101 

5,500,000 

17f 

200,000 

H 

1,400,000 

Hi 

6,000,000 

181 

220.000 

6 

1.600,000 

ill 

6,500,000 

181 

240.000 

H 

1.800,000 

124 

7.ooi),(ino 

191 

200,000 

H 

2.000.000 

12f 

7.- ".oo.  000 

191 

280,000 

H 

_'.  200,000 

L3 

8,000,000 

20| 

300,000 

H 

2.400,000 

13f 

8,500,000 

20| 

320, > 

H 

2,600,000 

131 

9,000,000 

21 

360,000 

n 

2. 800, 000 

141 

9,500,000 

21| 

400,000 

n 

3,000,000 

14J 

10.1100.(100 

450,000 

n 

.... 

NOTE.  —  Diameters  are  calculated   t->  nearest  eighths  of  an  Inch  with  a 
fihre  stress  of  5,000  lb6. 


108  The  Naval  Constructor 

D  =  draught  in  feet. 

B  =  greatest  distance  in  inches  from 

centre  of  pintle  to  back  of  rudder. 
5  =  greatest  breadth  of  rudder  in  inches. 

V  =  speed  in  knots. 

d  =  diameter  of  stock  in  inches. 

Then,  d  =  &y/Db  (2  B-b)V*. 

Rudder  Stock  per  Germanischer  Lloyd  Formula. 

This  rule  is  a  much  more  correct  one  than  Lloyd's  Register, 
using,  as  it  does,  truer  factors.  It  is  given  here  converted  for 
English  measure  as  well  as  for  metric. 

Let         d  =  diameter  of  stock  in  centimeters. 
F=  area  of  rudder  in  square  meters. 
r  =  distance  from  centre  of  gravity  of  area  to  axis  of 

stock  in  centimeters. 
V—  speed  in  knots. 

Then,  d  =  A2  {/ FrV2. 

For  English  measure  let 

d  =  diameter  of  stock  in  inches. 
A  =  area  of  rudder  in  square  feet. 
r  =  distance  from  e.g.  to  axis  in  inches. 

V  =  speed  in  knots. 

Then,  cZ  =  .103  AJArV*. 

British  Corporation  Formula. 

The  "B.C.,"  or  British  Corporation,  Rule  is  slightly  different 
from  the  foregoing,  but,  like  it,  takes  the  true  factors  into  account, 
and  gives  a  more  correct  result  than  either  of  the  foregoing  for- 
mulae. 

d  =  .26  ZJrAV*. 

Note.  —  "r"  is  here  taken  in  feet. 

PROPELLER    STRUTS. 

Simpson's  Formula. 

Propeller  "i"  brackets  or  struts  are  not  dealt  .with  in  any  of 
the  classification  societies'  rules,  and  in  deciding  on  a  suitable  area 
of  section  for  these,  it  is  the  invariable  practice  to  base  it  on  ex- 
perience.    Such  being  the  case,  a  great  divergence  is  found  in  the 


Propeller  Struts 


L09 


proportions  and  dimensions  of  them  in  vessels  of  similar  size  and 
power.  To  insure  greater  uniformity  in  their  design  and  weight 
consistent  with  ample  strength  to  meel  the  stresses  to  which  they 
are  subjected,  the  writer  has  prepared  the  formula  following,  based 
on  the  results  of  a  varied  experience  with  struts  for  all  sizes  of 
vessels  with  a  range  ol  I.U.P.  of  1U  to  7,000  per  shaft  and  revolu- 
tions of  To  t  i  600,  and  from  observation  of  some  which  were 
actually  carried  away.  It  should  be  stated  that  the  smaller  pow- 
ers were  not  for  twin  screws  but  for  small  eraft  with  cut-away 
deadwoods  necessitating  a  bracket  to  support  the  outer  end  of 
shaft.  From  the  formula  given,  the  area  is  obtained,  and  with  it 
the  following  proportions  determined  :  — 

SECTION   OF  ARM 


FORW'O. 
**>» 


FlG.  33. 


Let 


R  =  revolutions  of  engines  per  minute. 

/'  =  indicated  horse  power. 

Z=outboard    length   of   shaft  from  stern  tube   outei 

hearing  to  centre  of  boss,  in  inches, 
k  =  coefficient  =  .0633  R. 


Then, 


\/R  x  P      i 


k 


=.  area  in  square  inchi  3. 


Of  course  the  horsepower  is  that  transmitted  through  one  shaft 
only,  and  the  area  obtained  is  for  one  arm.  The  proportions  of 
the  pear-shaped  arm  are  as  under. 


n 

I 


,25 L.  7/ =.25  7?. 

.33  L.  r  =  .60B. 


For  the  lesser  powers  and  for  brackets  intended  for  wood  or 
composite  vessels,  the  brackets  should  be  of  gun  metal  or  bronze, 
and  for  higher  powers  and  steel  ships  of  cast  steel. 


110 


The   Naval   Constructor 


Spectacle  Frames. 

For  the  larger  classes  of  twin  screw  steamers  what  are  known 
as  spectacle  frames  are  bolted  to  body  post  to  take  the  outer  end 
of  shaft,  and  the  shell  plating  webbed  out  to  enclose  what  other- 
wise would  be  the  outboard  length  of  shafting,  as  described  in  the 
chapter  on  design.  These  frames  are  of  cast  steel  and  semi-pear- 
shaped  in  section.  The  area  of  this  section  may  be  found  from 
the  same  formula  as  if  the  ship  were  to  be  fitted  with  "^L" 


Fig.  39. 

brackets  and  the  result  multiplied  by  2.  This  greater  area  is 
accounted  for  by  the  fact  that  there ^  is  only  one  arm  and  the 
greater  breadth  of  same  required  to  permit  of  working  the  shell 
plating  and  also  obtaining  the  necessary  section  modulus.  The 
weight,  however,  will  be  found  to  approximate  very  closely  to  the 
open  struts.  Experiments  have  shown  that  better  results  are 
obtained  by  inclining  the  spectacle  frame  downwards  at  an  angle 
of  about  30°  from  the  horizontal. 


The   Transport  or  Cattle  111 


Proportions. 

A  =2  L.  F=  |  />. 

/;-.l.  2i  =  Length    of  pear-shaped 

C  =  B.  sect  inn  as  gut  for  ".1  " 

K  —  \  !>.  bracket. 

The  outside  diameter  JD  of  the  boss  will  be  fixed  in  conjunction 
with  the  engineer. 


THE   TRANSPORT    OP    CATTLE. 

In  arranging  the  ship  for  the  transport  of  cattle  in  conformity 
•with  the  United  States  Department  of  Agriculture,  care  should  be 
exercised  in  first  providing  for  the  main  cattle  gangways.  A  good 
location  for  these  would  be  at  the  ends  of  engine  or  boiler  casings 
opposite  which  the  cattle  doors  should  be  placed.  The  webs, 
webframes,  and  any  other  structural  obstructions  should  be  ar- 
ranged with  a  view  to  working  them  in  as  boundaries  for  blocks 
of  4  cattle  if  practicable,  and  if  the  ship  be  a  new  one,  the  frame 
spacing  should  be  fixed  to  work  out  with  the  legal  dimension  for 
cattle  pens  to  obviate  waste  of  space,  unsuitable  pillaring,  and 
division  boards  coming  off  beams.  If  the  ship  be  of  such  dimen- 
sion as  to  require  30"  spacing  ordinarily,  then  by  increasing  this 
to  30 1",  a  vi  tv  good  arrangement  of  pens  will  be  obtained.  Coal- 
ing ports,  mucking  ports,  and  all  thwartship  passages  in  connection 
therewith,  should  next  be  located,  bearing  in  mind,  in  arranging 
these,  the  4-cattle  blocks  previously  mentioned.  The  stalls  may 
be  then  outlined,  followed  by  the  pillars,  which,  of  course,  will  be 
placed  to  suit  these,  working  downwards  from  the  cattle  deck  to 
the  other  hold  pillaring. 

The  following  are  the  dimensions  of  cattle  spaces  required  by 
the  Department  of  Agriculture  : 

Cattle  per  head  on  upper,  spar,  or  weather  decks  : 

8'0"  lung  x  2't;"  wide  X  6'0"  high  in  the  clear. 

Cattle  loaded  under  decks  will  require  2  inches  more  width  unl 
in  regular  cattle  ships  with  satisfactory  ventilation. 

Pens  must  be  arranged  for  4  cattle,  unless  at  the  ends  of  a  row 
of  |  "tis.  where;  5  may  be  stow.  d. 

Special  permission  must  be  obtained  to  carry  cattle  on  lower 
deck,  and  in  all  cases  where  this  i<  granted,  the  width  allotted 
must  be  2' 8",  the  ventilation  sufficient,  and  no  animals  are  allowed 
on  hatches. 


112  The   Naval   Constructor 


Sheep,  per  head,  4'0"  long  X  14"  wide  in  the  clear.  Tens  must 
not  exceed  20  feet  x  8  feet  where  two  tiers  are  carried,  and  each 
tier  to  have  a  clear  vertical  space  not  less  than  3  feet. 

Horses,  per  head,  8  feet  long  X  2'6"  wide  X  6'3"  high  in  the  clear, 
and  as  far  as  possible  arranged  between  the  overhead  athwartship 
beams.  Each  horse  uinst  have  a  separate  stall,  and  where  22  or 
more  horses  are  carried,  a  hospital  8  feet  X  10  feet  square  must  be 
reserved. 

Alleyways  for  feeding  and  watering  to  be  8  feet  wide,  but  where 
obstructions  less  than  3  feet  long  occur,  and  at  ends  of  ship,  they 
may  be  reduced  to  a  minimum  of  18  inches. 

Thwartship  alleyivays  to  scuppers  to  be  18  inches  wide. 

Headboards  not  less  than  2  x  10  inches  or  3  x  8  inches,  of  spruce 
or  yellow  pine. 

Footboards,  same  dimensions  as  headboards. 

Division  boards  of  2x8  ii)ches,  spruce  or  yellow  pine  fitted 
vertically  for  cattle. 

Division  boards  for  horses,  2x9  inches  x  8  feet,  planed  and 
placed  horizontally. 

Footlocks,  2  inches  above  cement  X  4  inches  wide  of  spruce,  yel- 
low pine,  or  hardwood,  ranged  fore  and  aft,  and  placed  12  inches, 
14  inches,  26  inches,  and  14  inches  apart ;  the  first  one  being  12 
inches  distant  from  the  inside  of  footboard;  but  when  troughs  are 
used,  the  footlocks  will  be  placed  17",  16",  22"  and  16"  apart. 

Outside  planking  on  open  and  closed  rail  ships  to  be  not  less 
than  2  inches  spruce  or  \\  inches  yellow  pine. 

Ventilators.  Each  under  deck  compartment  not  exceeding  50 
feet  in  length,  must  have  at  least  four  18-inch  diameter  cowl  ven- 
tilators, with  tops  7  feet  above  shelter  deck,  two  being  placed  at 
each  end  of  the  compartment.  If  compartments  be  over  50  feet 
long,  additional  ventilators  must  be  fitted. 


Weight  of  Fittings  per  Head  of  Cattle  Carried. 

ITEM.  WE™  IN 

Cementing  on  deck  \\"  thick 185.00 

Total  woodwork,  including  bolts     ....  139.62 

Angle  steel  footlock  clips 11.43 

Castings  and  fittings,  including  bolts  .     .     .  37.19 

Gnawing  strips  of  segmental  iron    ....  6.00 

Solid  cattle  pillars         9.74 

Hollow  cattle  pillars           11.02 

Total  per  head  of  cattle       =400.00 


Weight  of  Hull  113 

Light.  Sufficient  light  must  be  provided  for  the  proper  tending 
of  animals  at  all  times. 

Ventilation  for  horses.  Under  deck  canvas  bags  should  be  fitted 
to  ventilators,  provided  with  iron  rings  at  bottom,  and  reaching 
within  18  inches  of  the  deck  under  foot. 

In  estimating  the  weight  of  cattle  fittings,  comprising  cement, 
cattle  pillars,  footlocks,  head  and  rumpboards,  castii 
following  will  be  found  reliable  :  — 

Weight  of  Fittings  per  Horse  Carried. 

It  Weight  in 

1TKM-  Lbs. 

Cementing  on  deck  li"  thick 185.00 

Total  woodwork,  including  bolts    ....  273.55 

Kicking  pieces  and  bolts 34.11 

Castings  and  fittings,  including  bolts  .     .     .  200.34 

Total  per  horse  |  London  regulation).     .  =693.00 
Leaving  an  American  port,  deduct  close  divi- 
sion boards 135.00 

Total  per  horse  (American  regulation)      =0.jS.UO 


WEIGHT    OF    HULL. 

In  estimating  for  displacement  purposes,  the  weight  of  a  ship's 
hull  is  usually  divided  broadly  into  two  parts,  viz.:  (1)  finished 
steel  and  (2)  weight  of  wood  and  outfit. 

There  are  various  methods  by  which  the  steel  may  be  estimated 
approximately,  but  where  great  accuracy  is  required  the  weights 
of  thestructure  should  be  calculated  in  detail  systematically,  and 
the  results  summarized  inconvenient  form  for  future  reference. 

The  arrangement  shown  in  the  table  will  be  found  useful  when 
the  cost  estimate  is  being  figured,  as  the  parts  of  structure  item- 
ized are  those  which  generally  show  variations  in  labor  pric 
The  summary  of  material  is  given  for  a  similar  reason,  ami  also 
for  the  variation  in  scrap  between  the  different  items. 

( >f  course  the  structural  parts  considered  in  the  table  must  each 
be  dealt  with  in  detail,  but  by  having  some  such  form  as  that 
here  presented  the  .chances  of  omission  will  be  minimized,  the 
weights  put  in  a  convenient  form  for  prime  cost,  and  also  usefully 
arranged  if  the  centre  of  gravity  should  afterwards  require  calcu- 
late _. 

The  most  common  method  to  approximate  the  weights  of  hull 
steel  when  there  is  insufficient  time  to  figure  in  detail,  is  to  take 
the  rati.)  between  the  weight  and  tb  c  number  of  a  known 


114 


The   Naval   Constructor 


Calculated  Finished  Steel  Weight. 


£ 

r-hf           tfc 

'A  x 

Part  of 

-.-  ~ 

Structure. 

•So  W 

Summary. 

X  " 

X^£ 

a* 

Ch2 

Tons. 

Tons. 

i 

Keel  bars  and  stem  .... 

3.5 

Forgings    . 

6.0 

2 

Stem  post,  rudder  frame  and 

20.0 

Angles  . 

587.0 

3 

Frames,  reverse  frames,  and 

doublings 

275.0 

Plates    . 

2063.6 

4 

Floors  and  tail  plates    . 

301.0 

5 

Beams  and  carlings       .     .     . 

225.4 

Bulb  tee     . 

168.4 

6 

Keelsons 

142.5 

7 

Bulkheads  (W.T.)    .... 

102.7 

Slips 

57.0 

8 

40.0 

9 

Engine  and  boiler  seats     . 

25.0 

Mouldings 

46.5 

10 

Shaft  tunnel  and  stools 

37.7 

11 

Inner  bottom  plating    .     .     . 

119.4 

Castings     . 

17.5 

12 

Shell  plating,  including  bhd. 

734  2 

Rivet  heads 

44.0 

13 

Rtrtnfffirs  a,nd  ties 

217.6 
305.3 

14 

Total      - 

2990.0 

15 

Cargo  and  coal  hatches     .     . 

37.5 

16 

Engine  and  boiler  casings 

77.6 

17 

Deck  houses 

140.0 

18 

Sundry  deck  and  hold  work  . 

25.0 

19 

Fresh-water  tanks   .... 

13.2 

20 

57.0 

21 

Moulding  and  copes 

46.5 

22 

Finished  steel  weight     .   = 

44.0 

2990.0 

vessel  of  similar  type  and  degree  of  fineness  and  use  the  coeffi- 
cient so  obtained  on  the  proposed  ship.  For  example,  a  known 
ship  of  length  330  feet,  breadth  41'  9",  and  depth  moulded  28'  3", 
has  a  total  steel  weight  of  1,680  tons,  then 

LxBxD     330X41.75X28.25 
8X100    = 1680  X  100         =  M  coeftcient- 

The  proposed  steamer  is  320  X  42  x  29 £  and  the  coefficient  of 
steel  weight  being  .431,  we  get 


Hull  Steel  Weights 


115 


320X42X291 

r^- x  .431  =  1 709  tons. 

This  rough  method  requires  good  judgment  and  practice,  as  it  is 
obvious  from  the  example  given  that  although  1,709  tons  is  a  fair 
approximation  it  is  still  too  heavy. 

Kecognizing  this  fact  and  the  necessity  for  a  quick  approxima- 
tive rule  which  would  give  fairly  close  results,  Mr.  J.  Johnson 
(vide  Trans.  Inst.  Nay.  Arch.  Vol.  31 »)  devised  a  method  based  on 
Lloyd's  longitudinal  number  (modified  for  some  types)  and  by 
plotting  down  known  steel  weights  opposite  their  numeral,  draw- 
ing curves  through  the  mean- values  of  each  type,  he  analyzed 
them  and  found  their  equations.  By  means  of  curves  prepared  in 
this  way  from  actual  weights,  the  amount  of  steel  is  easily  read  off 
and  the  increase  or  decrease  due  to  an  alteration  in  the  numeral  is 
readily  seen.     Johnson's  formula  is  as  under, 

W=cN*  or  W- 

where 

W  =  Finished  weight  in  tons  of  iron  or  steel  used  in  hull  construc- 
tion. 

N  =  Lloyd's  longitudinal  number  modified  as  follows  :  In  3 
decked  vessels  the  girths  and  depths  are  measured  to  the 
upper  deck  without  deduction.  In  spar  and  awning 
decked  vessels  the  girths  and  depths  are  measured  to  the 
spar  or  awning  decks  respectively. 
In  one.  two  or  well  decked  vessels  the  girths  and  depths  are 
taken  to  the  main  deck  in  the  usual  way. 

c  ami  K  are  coefficients  varying  with  different  types. 

X  is  an  exponent,  also  varying  with  different  types. 


Table    Giving    the    Mean    Values    for    c,    K,  and    x    for 
Vessels  Built  to  Lloyd's  or  Veritas'  Highest  Class. 


Type  of  Vessel. 

c. 

K. 

K> 

Three  deck,  with  complete  shelter  deck 
Three  deck 

.00359 
.00078 

.328 
.492 
.  570 
.666 

.856 
.410 

1.48 
1.40 
1.35 
1.30 
1.30 
1.40 

Spar  deck 

Awning  deck 

.00115 
.001*57 

One  deck,  two  deck,  and  well  deck 
Sailing  vessels 

.00215 
.00065 

J  16  The   Naval   Constructor 


Of  course  differences  in  the  arrangement  of  scantlings,  extent  of 
double  bottom,  number  of  bulkheads  or  length  of  erections  must 
be  calculated  as  extra. 

A  complete  set  of  curves  based  on  this  method,  but  extended  to 
embrace  the  largest  types  of  vessels  including  complete  shelter 
deck  steamers  is  given  opposite. 

The  second  part  of  the  finished  hull  weight,  viz.:  the  wood  and 
outfit,  embraces  everything  that  goes  to  finish  the  ship  excepting 
fresh  water,  coal  and  consumable  stores.  That  is,  it  comprises 
all  wood  work,  both  shipwright  and  joiner,  masts,  rigging,  sails, 
boats,  anchors,  chains,  cables,  hawsers,  furniture,  fixtures,  etc., 
many  of  the  items  being  extremely  difficult  of  accurate  cal- 
culation. For  this  reason  it  is  necessary  where  these  fittings  are 
calculated  in  detail  to  carefully  check  the  result  obtained  by  a 
similar  method  to  that  used  for  the  approximated  steel  weight 
from  actual  wood  outfit  data  derived  from  known  ships  of  similar 
type.  The  value  of  this  coefficient  for  various  classes  will  be 
seen  from  the  Table  of  Elements  of  Ships. 

Regarding  this  weight,  Johnson  states  that  it  wrill  be  found  to 
vary  almost  directly  as  the  longitudinal  number. 


Hull   Steel   Weights 


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Round  and   Square   Bars 


151 


STEEL. —  ROUND    AND    SQUARE    BARS. 
Sectional  Area  in  Inches  ;■;  3.4=  Weight  per  Lineal  Foot  in  /'<<)//<</*. 


-/•--' 

Weight  pee 

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Weight  per 

*  -  ' 

Lim:  \  i 

Foot  in 

gng 

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Area 

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2.245 

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13 

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41.65 

9.6211 

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8.301 

1.9175 

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33.89 

43.15 

9.9678 

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2.0739 

f 

35.09 

44.68 

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2.230,:, 

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8.178 

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37.55 

47.82 

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11.410 

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11.95 

2.7012 

2 

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lo. 10 

61.05 

11.793 

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10.024 

12.76 

2.9483 

H 

41.40 

52.71 

12.177 

152 


The   Naval   Constructor 


STEEL.  — ROUND    AND    SQUARE    BARS. 

Sectional  Area  in  Inches  x  3.4  =  Weight  per  Lineal  Foot  in  Pounds. 


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o 

Round. 

o 

Square. 
□ 

4 

42.72 

54.39 

12.506 

6 

96.1 

122.4 

28.274 

i 

1  6 

44.07 

56.11 

12.962 

i 

i  ij 

98.1 

125.0 

28.866 

1 
8 

45  44 

57.85 

13.364 

i 

8 

1,0  2 

127.6 

29.465 

3 

1  0 

46.83 

59.62 

13.772 

3 

1  6 

102.2 

130.2 

30.069 

1 
4 

48.23 

61.41 

14.186 

1 
4 

104.3 

132.8 

30.680 

5 

1  6 

49.66 

63.23 

14.607 

5 

1  6 

106.4 

135.5 

31.296 

a 

51.11 

65.08 

15.033 

a 

8 

108.5 

138.2 

31.919 

1  6 

52.58 

66.95 

15.466 

7 
1  6 

110.7 

140.9 

32.548 

1 

2 

54.07 

68.85 

15.904 

1 
2 

112  8 

143.6 

33.183 

9 
1 6 

55.59 

70.78 

16.349 

9 

115.0 

146.5 

33.824 

5 
§ 

57.12 

72.72 

10.800 

5 

8 

117.2 

149.2 

34.472 

1  1 
1  6 

58.67 

74.70 

17.257 

1  1 
1  6 

119.4 

152.1 

35.125 

3 

4 

60.25 

76.71 

17.721 

2. 

4 

121.7 

154.9 

35.785 

1  3 
16 

61.84 

78.74 

18.190 

1  3 
1  6 

123.9 

157.8 

36.450 

7 

8 

63.46 

80.80 

18.665 

7 
8 

126.2 

160.7 

37.122 

1  5 

1  6 

65.10 

82.89 

19.147 

1  5 

1  6 

128.5 

163.6 

37.800 

5 

66.76 

85.00 

19.635 

7 

130.9 

166.6 

38.485 

i 

1  6 

68.44 

87.14 

20.129 

i 

16 

133.2 

169.6 

39.175 

1 

8 

70.13 

89.30 

20.629 

1 

135.6 

172.6 

39.871 

3 

1  6 

71.86 

91.49 

21.135 

3 

1  6 

137.9 

175.6 

40.574 

1 
4 

73.60 

93.72 

21  648 

1 

4 

140.4 

178.7 

41.282 

5 
1  6 

75.37 

95.96 

22.166 

5 

1  u 

142.8 

181.8 

41.997 

3 
g 

77.15 

98.22 

22.691 

3 

8 

145.2 

184.9 

42.718 

_7_ 

1    ft 

78  95 

100.5 

23.221 

>7 
/ 

1  6 

147.7 

188.1 

43.445 

±   O 

1 
2 

80.77 

102.8 

23.758 

1 

2 

150.2 

191.3 

44.179 

9 
1  6 

82.62 

105.2 

24.301 

9 

16 

152.7 

194.4 

44.918 

5 
§ 

84.48 

107.6 

24.850 

5 

8 

155.2 

197.7 

45.664 

1  1 

1  6 

86.38 

110.0 

2- '..406 

1  1 

157.8 

200.9 

46.415 

3. 
4 

88.29 

112.4 

25.967 

3 
4 

160.3 

204.2 

47.173 

13 

1  6 

90.22 

114.9 

26.535 

1  3 

1  6 

163  0 

207.6 

47.937 

7 
g 

92.16 

117.4 

27.109 

7 
8 

165.6 

210.8 

48.707 

15 

16 

94.14 

119.9 

27.688 

1  5 
1  6 

168.2 

214.2 

49.483 

Steel   Weights 


L53 


WEIGHTS. 


Half-Round,  Hollow  Half-Round,  Feather 
Edge,  and  Convex. 


Dbs<  lxii-- 

TIOK. 


Size. 


■  •Itli. 


Thick- 


6 
5} 

5' 
4i 
4" 

32 

*">  i 

Si 

3 

23 

2i 

21 
2 

If 

1\ 

H 
l 


4 
3| 

3i 

3| 
3 

2* 

2" 

n 


-i 

L". 


If 
L| 

11 

11 

i 

7 

s 

I 

f 


n 


9 


* 

i 


Weight 

per 
Lineal 
Foot. 

48.07 

40.39 

.33.38 

27.04 

21.36 

18.78 

16.30 

14.11 

L2.02 

10.10 

8.34 

6.75 

:.  34 

4.09 

300 

2.(19 

1.34 


18.36 

15.78 

13.36 

B.83 

8.01 
7.35 
6.68 
5.34 
3.26 
2.25 


■)  1 

-   . 

8 

•J  I 

1 

-1 

\ 

2 

1 

2 

A 

2 

8 

If 

1 

1', 

U 

1 

H 

ITf 

ii 

3.73 
2.98 
2.69 
2.39 

2.o'.» 

1.79 
1.57 
1.34 
1.23 
.93 
.85 


Dl    *<   KIP 
I  LON. 


Size. 


6 


Breailtli 


2i 

L". 
2', 

-!• 
2 

2 

2 
2 

1| 
If 

i! 
if 

13 
li 

li 

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11 
11 
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II 

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13 
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3 

I  i 

T6 

5 

3. 
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9 

16 

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a 


9 

16 


3 

5 

- 

9 
T6 

i 

3 
I 

1  1 


9 

1  6 

1 

s 


- 


1 

T7* 


Weighl 

per 

Lineal 

Foot. 


7.17 
6.64 
6.11 
5.58 
5.05 
4.52 
3.98 
4.30 

3.  I.") 
3.03 
2.60 
3.76 
3.02 
2.65 
2.28 
3.25 
2.62 
2.30 
1.98 
2.99 
2.70 
2.41 
2.12 
1.82 
1.72 
1.46 
1.19 
1.56 
L.32 
L.09 


154 


The  Naval  Constructor 


WEIGHT   OF    SHEET   STEEL. 


O  0 

Birmingham  Wire 

Gauge  and  English 

Standard  Gauge. 

American  (B.  &  S.) 
Wire  Gauge. 

New  U.S.  Stand- 
ard Gauge,  1873. 

Thickness 
in  Inches. 

Weight 
per  Sq.  Ft. 

18.52 

Thickness 
in  Inches. 

Weight 
per  Sq.  Ft. 

18.76 

Thickness 
in  Inches. 

.406 

Weight 
perSq.Ft. 

0000 

.454 

.460 

16.58 

000 

.425 

17.34 

.410 

16.72 

.375 

15.30 

00 

.380 

15.50 

.365 

14.88 

.344 

14.03 

0 

.340 

13.87 

.325 

13.26 

.313 

12.75 

1 

.300 

12.24 

.289 

11.80 

.281 

11.48 

2 

.284 

11.59 

.258 

10.52 

.266 

10.84 

3 

.259 

10.56 

.229 

9.36 

.250 

10.20 

4 

.238 

9.71 

.204 

8.33 

.234 

9.56 

5 

.220 

8.98 

.182 

7.42 

.219 

8.93 

6 

.203 

8.28 

.162 

6.61 

.203 

8.29 

7 

.180 

7.34 

.144 

5.88 

.188 

7.65 

8 

.165 

6.73 

.129 

5.24 

.172 

7.01 

9 

.148 

6.04 

.114 

4.66 

.156 

6.38 

10 

.134 

5.47 

.102 

4.15 

.141 

5.74 

11 

.120 

4.89 

.091 

3.70 

.125 

5.10 

12 

.109 

4.44 

.081 

3.29 

.109 

4.46 

13 

.095 

3.87 

.072 

2.93 

.094 

3.83 

14 

.083 

3.38 

.064 

2.61 

.078 

3.19 

15 

.072 

2.94 

.057 

2.32 

.070 

2.87 

16 

.065 

2.65 

.051 

2.07 

.063 

2.55 

17 

.058 

2.37 

.045 

1.84 

.056 

2.30 

18 

.049 

1.99 

.040 

1.64 

.050 

2.04 

19 

.042 

1.71 

.036 

1.46 

.044 

1.79 

20 

.035 

1.42 

.032 

1.30 

.038 

1.53 

21 

.032 

1.30 

.028 

1.16 

.034 

1.40 

22 

.028 

1.14 

.025 

1.03    . 

.031 

1.28 

23 

.025 

1.02 

.023 

0.921 

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1.15 

24 

.022 

0.808 

.020 

0.821 

.025 

1.02 

25 

.020 

0.816 

.018 

0.729 

.022 

0.89 

26 

.018 

0.734 

.016 

0.651 

.019 

0.77 

27 

.016 

0.653 

.014 

0.581 

.017 

0.70 

28 

.014 

0.571 

.013 

0.515 

.016 

0.64 

29 

.013 

0.531 

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0.459 

.014 

0.57 

30 

.012 

0.489 

.010 

0.409 

.013 

0.51 

31 

.010 

0.408 

.009 

0.364 

.011 

0.45 

32 

.009 

0.367 

.008 

0.324 

.010 

0.41 

33 

.008 

0.326 

.007 

0.288 

.009 

0.38 

34 

.007 

0.286 

.006 

0.257 

.009 

0.35 

35 

.005 

0.204 

.006 

0.228 

.008 

0.32 

36 

.004 

0.162 

.005 

0.204 

.007 

0.29 

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T 


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C.G.   by   Experiment  171 


Lloyd's  Bulb  Sections. 

The  depth  in  inches  D  of  the  section  to  be  the  base  from  which 
to  deduce  the  other  dimensions. 

The  width  of  the  bulbs  to  be  2\C  for  bulb  angles,  and  S\C  for 

bulb  plates  and  tees,  when  C  is  '"*  in  the  case  of  bulb  angles, 

and  for  bulb  plates  and  tees.     The  form  of  the  bulbs  to  be 

in  accordance  with  the  sketches. 


7\ 


z 
o 

> 

-o 
n 

33 


Fig.  44. 

The  standard  thickness  for  regulating  the  widths  of  bulb  of 
beams  and  bars  whose  depth  is  not  an  exact  number  of  inches, 
should  correspond  to  the  depth  in  inches  next  below  the  actual 
depth,  thus  —  for  tee  beams  and  bulb  plates  104  inches  depth,  the 
standard  thickness  to  be  used  in  determining  the  dimensions  of 

10  +  1       11 

20-OT20 


the  bulb  should  be    -^ —  or  —  -   See  figures  44  and  45. 


C.G.  BY  EXPERIMENT. 

All  finished  vessels  should  be  inclined  before  leaving  the  build- 
er's hands  and  their  exact  centre  of  gravity  found  experimentally. 
The  value  of  this  information  cannot  be  over-estimated,  although 
in  many  cases  where  possessed  it  does  not  seem  to  be  applied  with 
the  care  its  importance  demands,  as  evidenced  by  the  proportions 
of  many  ships  of  the  merchant  marine. 


172 


The  Naval  Constructor 


Fig.  45. 

The  principle  on  which  the  experiment  is  based  will  be  under- 
stood from  a  reference  to  Fig.  46,  where  p  is  a  small  weight  placed 
on  deck  at  centre  line,  and  afterwards  shifted  to  either  side 
through  a  distance  a.  The  centre  of  gravity  before  the  movement 
was  made  is  shown  at  G.  It  will  be  evident  that  this  centre  after 
the  weight  has  been  shifted,  will  move  to  a  new  location  parallel  to 
the  line  of  shift,  and  that  the  weight  multiplied  by  the  distance 
through  which  it  has  been  moved,  will  give  a  moment  equal  to 
the  weight  of  the  whole  ship  by  the  distance  the  common  centre 
of  gravity  G  has  been  moved  to  G±,  so  that  we  get :  — 

GQ      P*at 
Before  attempting  to  carry  out  the  inclining  experiment,  the 


C.G.   by   Experiment 


173 


following  preparations  should  be  made,  observing  that  although 
not  imperative  that  the  vessel  be  completely  finished,  it  is  well  to 
have  her  in  that  condition  if  possible.  The  bilges  should  be 
carefully  examined  to  see 

that  they  are   perfectly  (  j* a >j 

free  from  loose  water,  and 

the  boilers,    condenser, 

fresh    water    and    ballast 

tanks  must  be  either  empty 

or  pumped  up  "chock 

full."  as  any  free  water  in 

the  ship  will   destroy  the 

value  of  the   experiment. 

All  workmen,  unless  those 

assisting,    must   be   sent 

ashore,  and  when  the  shift 

is  being   measured  the 

assistants   and    laborers 

should  be  lined  up  on  centre  line  of  ship,  a  position  they  shall 

have  occupied  before  beginning.     The  weather  should  be  perfectly 

calm,  and  an  enclosed  space  of  water  as  a  basin,  or  dock,  selected, 

and  the  mooring  lines  eased  off  slack  to  permit  the  vessel  to  move 

freely. 

The  inclining  weights  should  aggregate  .5  to  one  per  cent  of 
the  displacement,  and  two  parallel  lines  should  be  marked  off  on 
deck  amidships,  representing  the  distance  through  which  the  centres 
of  gravity  of  the  weights  shall  be  moved.  A  suitable  position 
must  be  obtained,  say  in  the  engine  or  boiler  hatch,  in  which  to  fix 
a  large  tee  square  with  the  cross  head  placed  downwards,  and  a 
plumb  line  and  bob  attached  at  the  end  of  the  blade,  care  being 
taken  that  the  bob  swings  clear  of  the  square.  When  these  prep- 
arations have  been  made  and  the  inclining  weights  placed  on  deck, 
an  accurate  draught  should  be  taken  and  the  men  ranged  up  on 
centre  line,  when  a  plumb  line  may  be  marked  off  on  the  edge  of 
square  as  a  starting  point,  the  weights  being  thereafter  transferred 
from  the  centre  line  to  port  or  starboard  and  an  observation  made. 
The  weights  should  then  be  moved  right  over  to  the  opposite  side, 
and  the  inclination  noted.  As  a  final  check  on  the  total  shift  the 
weights  may  be  shifted  back  to  their  original  position,  when  of 
course  the  plumb  line  should  cover  the  point  originally  marked  on 
starting.  From  the  following  data  procured  we  shall  be  enabled 
to  calculate  the  centre  of  gravity  on  the  principle  previously  re- 
ferred to,  viz.:  — 

(1)  Draught  of  water. 

(2)  Displacement  from  the  foregoing. 


174 


The  Naval  Constructor 


(8)   Weights  shifted. 

(4)  Distance  between  the  two  lines  representing  the  space 
through  which  weights  were  shifted. 

(5)  Length  of  plumb  line  from  point  of  suspension  to  edge  of 
square. 

(6)  Travel  of  plumb  line  from  port  to  starboard,  and  starboard 
to  port.     Take  mean. 

(7)  Condition  of  the  ship  as  regards  state  of  completion  aud 
what  weights  as  cargo,  coal,  fresh  water,  water  in  boilers, 
ballast  tanks  and  dunnage  are  on  board. 

As  the  vessel  has  been  previously  slacked  off,  on  shifting  the 
weights,  it  will  be  apparent  that  the  ship  will  heel  over  so  that  the 
centre  of  gravity  G,  and  the  centre  of  buoyancy  B\  (Fig.  47),  will 
be  in  the  same  vertical  line  and  M  will  be  the  nietacentre.  Let 
a  represent  the  angle  of  heel,  then  :  — 


Fig.  47. 


The  tangent  of  a  is  found  by  taking  the  length  of  plumb  line 
"J.  5"  and  the  mean  shift  of  bob  "BE"  on  tee  square,  from 
which  we  get :  — 

AB 

tana  =  M ' 

The  triangle  GMGf  and  BAE  are  similar,  then 

GG\      BE 

■ =  — — i  ' 

GM      AB 

_,_        GMXBE      Pxa 

GrGrj  = 


AB 


and 


p  x  a 


CM=pXay.AB  = 

D        BE     D  x  tan  a 


Centre  of  Gravity. 


175 


The  height  of  M  may  be  calculated  for  the  draught  with  which 
we  are  dealing  or  directly  measured  from  the  metacentric  diagram, 
and  the  GM  as  obtained  above  deducted  from  this  height  will  give 
the  centre  of  gravity  above  base  at  the  time  of  the  experiment. 
This  height  of  course  will  require  correction  by  deducting  the 
inclining  weights  and  the  excess  water  in  boilers,  if  these  have 
been  pumped  chock  full  for  the  experiment. 

Centre  of  Gravity. 

The  vertical  centre  of  gravity  of  a  ship  is  probably  the  most  im- 
portant point  which  the  naval  architect  has  to  determine,  as  well 
as  the  most  difficult  to  calculate  with  accuracy.  Therefore  it  is 
that  the  calculation  of  this  centre  in  detail  is  only  resorted  to 
when  insufficient  data  derived  from  a  somewhat  similar  type  is 
wanting,  as  the  most  reliable  method  is  that  computed  from  actual 
centres  obtained  from  experiments.  However,  where  this  is  not 
obtainable,  the  calculation  in  detail  by  careful  working  out  and 
good  judgment  should  give  equally  accurate  results.  Where  the 
former  method  is  resorted  to.  the  table  of  coefficients  given  in  the 
chapter  on  Design  will  be  found  of  service,  observing  that  these 
are  for  the  finished  vessel  loaded  with  a  homogeneous  cargo. 

When,  however,  it  is  imperative  to 
detail,  the  simplest  method  will  be  to  treat 
shell  of  uniform  thickness,  and  when 
the  centre  of  gravity  as  such  is  as- 
certained, to  make  the  necessary  ad- 
ditions for  excesses  on  particular 
strakes,  keelsons,  beams,  deck  plat- 
ing, superstructure  and  wood,  outfit 
and  equipment  weights.  The  centre 
of  gravity  of  the  machinery  with  steam 
up  will  be  furnished  by  the  engineers. 

On  a  body  plan  of  ten  sections 
with  half-end  ordinates,  mark  off 
around  the  half  girths  of  each  section 
a  spot  every  two  feet  apart,  as  shown 
on  Fig.  48.  dropping  a  perpendicular 
line  from  these  locations  to  the  base. 
Measure  these  heights  above  the  base 
and  tabulate  them  for  each  section, 
calling  the  centre  line  "  0  "  as  in  the 
table.  One  side  only  need  be  dealt 
with,  as  the  ship  is  symmetrical  about  the  middle  line. 

Each  of  the  ten  sections  having  been  treated  in  a  like  manner  to 
the  foregoing,  and  the  individual  centres  of  gravity  of  all  deter- 


into  the  calculation  in 
the  hull  proper  as  a 


176 


The  Naval  Constructor 


Section  No.  5. 

Station. 

Heights. 

Multipliers. 

Functions. 

0 

l 

2 

1 

.6' 

2 

1.2 

2 

1.3' 

1 

1.3 

3 

2.4' 

2 

4.8 

4 

4.1' 

1 

4.1 

5 

6.1' 

2 

12.2 

6 

8.2' 

1 

4.1 

•      •      ■ 

9 

)27.7 
3.07' 

£ 

,.07'=C.G. 

of  No.  5  above  base. 

mined,  these  centres  are  then  tabulated  and  the  common  centre  of 
gravity  found  by  a  similar  operation  to  the  above,  i.e.,  they  are  in- 
tegrated by  Simpson's  multipliers,  and  the  sum  of  the  functions  so 
obtained  divided  by  the  sum  of  the  multipliers,  when  the  resulting 
quotient  will  be  the  perpendicular  height  of  the  common  centre  of 
gravity  of  all  the  sections  or  of  a  shell  of  uniform  thickness. 

Vertical  Centre  of  Gravity  of  Shell. 


Sections. 

C.G.  of  Sec- 
tions 
above  Base. 

Simpson's 
Multipliers. 

Functions. 

0 

1 

1 

2 
3 

4 
5 

6 

7 
8 
9 

9^ 
10 

•      •      • 

6.00 
5.21 
4.16 
3.50 
3.36 
3.20 
3.07 
3.56 
3.93 
4.20 
4.66 
5.00 
5.74 

i 

4 

1 

3 
4 

2 

1 

2 
1 

2 
1 

2 

3 
4 

1 
1 

15 

1.50 
5.21 
3.12 
7.00 
3.36 
6.40 
3.07 
7.12 
3.93 
8.40 
3.49 
5.00 
1.43 

)  59.03 

3.94' 

3.94'=  Mean  C.G.  above  base. 

Centre  of  Gravity 


177 


Another  method  to  obtain  the  vertical  height  of  C.G.  due  to 
form  for  a  shell  of  uniform  thickness  is  to  take  the  sum  of  the 
functions  of  water  line  half-breadths  of  all  sections  from  base  to 
gunwale,  and  divide  them  by  the 
sum  of  the  multipliers  used,  which 
will  give  a  mean  half-breadth  for 
each  water  plane.  By  plotting  off 
these  mean  dimensions,  a  mean 
section  of  the  ship  may  be  drawn 
on  stout  paper,  cut  out  with  a 
penknife,  then  pinned  to  port  and 
starboard  alternately  and  swung 
on  a  board  having  a  plumb  line 
scribed  on  as  shown  in  Fig.  49. 

The  intersection  of  the  mark 
points  A  and  B  with  the  plumb 
line,  should  be  joined  with  the  pin 
holes  C  and  D.  and  where  they 
cross  each  other  on  centre  line  will 
be  the  mean  height  of  centre  of  gravity.  Carefully  done,  this 
will  give  a  very  close  approximation  to  the  calculation.  Of  course 
the  usual  additions  as  mentioned  in  the  preceding  method  will  be 
required  to  calculate  the  actual  C.G.  of  vessel. 

Outfit  in  detail,  stores,  fresh  water,  coal,  etc.,  will  be  set  down, 
giving  the  weight  and  estimated  height  of  their  respective  centres 
of  gravity  from  base,  when  the  sum  of  the  moments  produced 
divided  by  the  total  weight  will  give  a  resulting  quotient  equal  to 
the  mean  height  of  C.G.  of  ship  from  base  without  cargo,  the 
centre  of  gravity  of  which  may  be  found  by  a  similar  experiment,  as 
it  is  customary  to  treat  this  as  being  of  a  homogeneous  character. 


Fig.  49. 


178  The   Naval   Constructor 

CHAPTER  VII. 

STRENGTH    OF    SHIPS. 

It  is  not  generally  considered  necessary  to  make  strength  calcu- 
lations for  an  ordinary  merchant  vessel  when  the  scantlings  are  in 
accordance  with  any  of  the  classification  societies'  rules,  but  in  the 
case  of  a  special  design,  and  also  in  warships,  it  is  advisable  to  do  so. 

In  these  calculations,  the  ship  is  considered  as  a  girder  and  the 
principle  is  the  same  as  that  of  a  beam  supported  at  both  ends,  or 
only  at  the  middle,  as  may  be  the  case  for  "  sagging  "  or  "  hog- 
ging" respectively,  uniformly  loaded  but  unevenly  distributed. 
As  it  is  practically  impossible  to  determine  accurately  the  amount 
of  stress  that  a  ship  will  be  subjected  to  when  laboring  in  a  sea- 
way, it  would  seem  quite  legitimate  to  arrive  at  the  necessary 
conclusions  on  the  basis  of  comparison  with  other  ships,  which 
have  proved  to  be  sufficiently  strong,  and  this  is  what  is  usually 
done  in  practice.  In  order  that  this  information  may  be  of  use 
for  comparative  purposes,  it  is  advisable  to  lay  off  the  curves  of 
weight,  buoyancy,  bending  moments,  etc.,  to  some  standard 
length  and  the  mean  weight  or  buoyancy  ordinate  to  some  stand- 
ard height,  so  as  to  make  the  diagram  as  convenient  as  possible. 

Curve  of  Weights. 

The  mean  weight  per  foot  of  length  of  the  total  hull  is  calcu- 
lated at  convenient  distances  apart  and  these  set  up  as  ordinates 
from  the  base  line  of  the  diagram,  at  their  corresponding  stations, 
taking  care  to  use  the  proper  scale  as  previously  determined  on  ; 
the  other  heavy  weights,  as  guns,  armor,  machinery,  coal,  homo- 
geneous cargo,  etc.,  are  calculated  separately  and  added  as  rect- 
angles above  the  curve  of  hull  weights.  A  mean  curve  is  then 
run  through  these  points,  taking  care  that  its  centre  of  gravity 
comes  over  the  centre  of  buoyancy  and  that  the  area  circumscribed 
by  the  curve  equals  the  displacement  of  the  ship. 

Curve  of  Buoyancy. 

The  displacement  in  tons  per  foot  of  length  is  then  calculated  at 
suitable  intervals  apart  and  set  up  as  ordinates  in  the  same  man- 
ner as  for  the  weight  curve.  The  area  enclosed  by  a  curve  pass- 
ing through  these  spots  should  also  equal  the  displacement  of  the 
vessel  and  will  show  the  distribution  of  the  support  given  by  the 
fluid  pressures  in  relation  to  the  curve  of  weights  at  any  point  in 
the  snip's  length. 


Strength  of  Ships 


179 


180 


The  Naval  Constructor 


Calculation  Table  for 


Moment  of  Inertia  of  Section 

Item. 

Size. 

Gross 
Area. 

Net 

Area  = 

A. 

Sq.  In. 

Sq.  In. 

Bar  keel  (h) 

6"  x  3" 

18.0 

14.3 

Flat  plate  keel  (|)     .     .     .     . 

27"  x  \%" 

81.1 

22.1 

Garboard  strake  A  . 

48"  —  2  0// 

°               20 

48.0 

38.0 

Strakes  B,  C,  D,  and  E     .     . 

4- 51"  X  if" 

173.4 

139.4 

Strake  F 

48"  x  if" 

432     . 

35.1 

Strake  G 

60"  x  H" 

540 

43.2 

Strake  H 

54"  X  \r 

48.0 

38.7 

Strake  J 

00"  XH" 

54.0 

43.2 

Strake  K 

54"  x  if" 

48.0 

38.7 

Strakes  M,  N,  0,  P,  and  E    . 

5  (54"  x  l-i") 

229.5 

183.0 

Strakes  £  and  T 

2  (44"  x  if") 

97.2 

174 

Strake  Z7  (sheer) ....      j 

51"  x  ff" 
37.5"  xlf 

51.0) 
37.51 

09.5 

Strake  W 

sif'xff" 

51.7 

40.7 

Strake  X  (sheer)  .... 

51"  x  ff" 

37.5"xf§" 

51.0  I 
37.5$ 

69.5 

Strakes  Y  and  Z 

2-51"  x  if" 

51.0 

40.6 

f  Keelson  (i) 

58"  x  M" 

21.7 

18.0 

f  Keelson,  bottom  angle    .     . 

5"x  5"x|f 

7.4 

5.6 

f  Keelson,  top  angle      .     .     . 

4"x4"x  if" 

4.8 

3.5 

First  longitudinal     .... 

47"  x  ^" 

23.5 

4.5 

Second  longitudinal       .     . 

44"  x  if" 

22.0 

4.5 

Third  longitudinal    .... 

401"  v  io// 

"±"2       A    2  0 

20.2 

4.5 

Margin  plate 

58"  x  if" 

40.0 

30.1 

Margin  angle 

4"x4"x  |f" 

4.8 

3.5 

Inner  bottom  strake  A  (^) 

30"  x  if" 

19.5 

16.1 

Inner  bottom  strakes,  B,  C,  D, 

. 

.Zv,  F 

279. 5"  xH" 

153.7 

131.2 

Tie  plate 

33" x  if" 

19.8 

15.6 

Bilge  keel  angles 

2_6"X4"xig" 

9  5 

7.6 

Bilge  keel  plate 

10"  x  if" 

9.0 

8  5 

Lower  hold  stringer       .     .      j 

2  [  10"x3i"x48" 
'  10"  x  if" 

J  21.6 

19.6 

Table  for   Moment  of  Inertia 


181 


Moment  of  Inertia. 


at  Frame  M  am>  at  Fkamk  If. 

Arm 

=  </. 

MollH'llt 

=  </A. 

Moment 
of  Inertia 

=  d-A. 

-  fi    . 

-  :•  -  - 
— *~ ' —  '. 

°  r-         — 
--r      II 

Square  of 

Depth  =  hn-. 

A  Net 
Area= 

A 

A  Ah*. 

Ft. 

Ft.    Sq.  In. 

Fl.-S|.ln. 

Ft.2 

Sq.  In. 

Ft.'SqJn. 

-26.71 

-382 

10,202 

•        >        • 

.    .    . 

.   .   . 

-  26.59 

-588 

15,625 

•        •        • 

.    .    . 

.   .   . 

-  26.30 

-499 

26,285 

■         •        • 

.    .    . 

.  .   . 

-25.55 

-3,562 

91,000 

•         ■        • 

.    .    . 

.   .   . 

-  24.60 

-863 

21.241 

•        •        • 

.    .    . 

... 

-  24.00 

-1,087 

24,883 

•        •        • 

.    .    . 

.    .    . 

-  22.05 

-853 

18,816 

3 

'  9 

3.2 

29 

-  18.65 

-806 

15,026 

4.50 

20.3 

3.6 

73 

-  14.45 

-559 

8,081 

4.50 

20.3 

3.2 

65 

-    2.7"> 

-503 

1.383 

20.50 

420.25 

15.25 

6,409 

11.30 

875 

9,883 

8.5 

72.25 

6.45 

466 

17.10 

1,188 

20,322 

(4.25 
(3.12 

18.06 
9.73 

3.3} 
2.5  J 

84 

20.75 

845 

17,524 

4.30 

18.49 

3.4 

63 

24.50 

1,703 

41,717 

(4.25 
(3.12 

18.06 
9.73 

3.8) 
2.5* 

84 

30.10 

1,222 

36,784 

8.00 

64.00 

3.4 

218 

-  24.10 

-434 

10,454 

4.83 

28.33 

1.5 

35 

-  26.35 

-148 

3,888 

•      •      • 

•      •      •      • 

•      •      • 

•      •      • 

-21.75 

-76 

1,656 

*      •      • 

•      •     •     • 

•      •      • 

•      •      • 

-23.70 

-107 

2,528 

3.92 

15.37 

.4 

6 

-23.25 

-105 

2,433 . 

3.67 

13.47 

.4 

6 

-22  80 

-103 

2,339 

3.37 

11.36 

.4 

5 

-  22.00 

-662 

14,568 

3.67 

13.47 

2.5 

3.4 

-24.10 

-84 

2,033 

.... 

.   .  . 

... 

-21.55 

-347 

7,477 

.... 

.  .  . 

.  .  . 

-21.05 

-2,762 

58.135 

.   .   .   • 

.   .  • 

.  .   . 

-  20.33 

-317 

6.447 

.   .   .   . 

.   .   . 

.   .   . 

-  22.60 

-172 

:i.882 

.   .  .   • 

.   .   . 

.  .   . 

-  23.00 

-196 

4,496 

.... 

.   .  . 

•      •      • 

-  15.60 

-306 

4,771 

.... 

.   .   . 

.   .  . 

182 


The   Naval   Constructor 


Calculation  Table 

for  Moment 

Moment  of  Inertia  of  Section 

Item. 

Size. 

Gross 
Area. 

Net 

Area  = 

A. 

2  [  10//x3i//x48// 

j  Sq.  In. 

Sq.  In. 

Upper  hold  stringer .... 

L                                     & 

10"  x  ft" 

21.6 

19.6 

Orlop  deck  stringer  .... 

4Q//  v    13// 

31.9 

27.9 

Orlop  deck  stringer  angle  . 

4"  x  4"  x  \\" 

4.1 

3.1 

Orlop  deck  plating    .... 

229"  x  2V" 

80.2 

69.7 

Lower  deck  stringer      .     .     . 

49"  x  W' 

31.9 

27.9 

Lower  deck  stringer  angle 

4"  x  4"  x  U" 

4.1 

3.1 

Lower  deck  plating  .... 

229"  X  Jo" 

91.6 

79.6 

Lower  deck  ridge  bar    .     .     . 

9"x3.85"xi§"[ 

7.9 

7.0 

Middle  deck  stringer     .     .     . 

49"  x  M" 

39.2 

33.6 

Middle  deck  stringer  angle     . 

4"  x  4"  x  H" 

4.1 

3.1 

Middle  deck  plating      .     .     . 

233"  X  2V 

104.9 

91.4 

Middle  deck  ridge  bar  .     .     . 

9"x3.85"xi£"[ 

7.9 

7.0 

Upper  deck  stringer      .     .      j 

41"  x  |ft" 

50"  x  \%" 

41.0) 
45.0  i 

72.9 

Upper  deck  stringer  angle 

5"  x  5"  x  W 

5.6 

4.3 

Upper  deck  plating  .     .     .      j 

139"  xW    I 

GO"  x  U"     ' 

115.5 

101.1 

Upper  deck  ridge  bar    .     . 

8"  x  3i"  x  W'  [ 

7.0 

6.1 

Shelter  deck  stringer     .     .      j 

50"  x  M" 
94"  x  W 

45.0/ 
75.2  J 

102.7 

Shelter  deck  stringer  angle     . 

2_5"x5"x|£" 

16.4 

12.4 

Shelter  deck  plating      .     .      j 

135"  x  M" 

58"  xM" 

j  131.3 

114.3 

Shelter  deck  ridge  bar  . 

8"  x  3  \"  X  M"  [ 

7.0 

6.1 

Bridge  deck  stringer 

KO//  v     9  " 

23.4 

20.0 

Bridge  deck  stringer  angles     j 

7//  v  31"  V  1  2" 
<        A  "9       ^20 

Ql//  v   31"  v"    8  " 

°2~      A  O^      X   20 

}    8.6 

7.3 

Bridge  deck  plating .... 

246"  x  io" 

61.5 

50.5 

2,515.3 

2,036.9 

2,370.8 

1,918.5 

Moment  of  Inertia  of  Section  at  Frame  M. 

Assumed  neutral  axis  26.5'  above  base. 

Actual  neutral  axis  =  \%\%  =  1.28'  above  assumed  neutral  axis  =  27.78' 

above  base  line. 
Moment  of  inertia  about  correct  neutral  axis  =  2  (810,320  -f-  7,577  —  3,341) 

=  1,629,112  Ft.2  Sq.  In. 
Note.  —  Rivets  neglected  botb  in  compression  and  tension. 


Table  for   Moment  of  Inertia 


183 


of  Inertia.  —  (Continued.) 


at  Frame  m  and  at  Fbame  a 


Ann 
=  <l. 


Ft. 
11.35 

6.40 
6.35 
6.00 
1.00 
1.70 
2.00 
1.25 
9.67 
9.75 
10.00 
9.25 

17.70 

17.70 

18.10 

17.15 

25.75 

25.60 

26.10 
25.15 

33.65 

33.75 
.34.05 


•      •      • 


Moment 

=  (IA. 


Ft.    Sq.  In. 

—222 

-179 

-20 

-418 

45 

5 

159 

9 

325 

30 

914 

05 

1.290 

70 

1,830 

105 

2.045 

317 

2.983 
1 53 

673 

246 

1.720 


(  +19,423  I 
\  —16,010  | 

2,613 
i  -f  15,562  i 
\  —16,810  j 

-1,248 


Moment 
of  [nertia 

—  (PA. 


Ft.~Sq.lll. 

2,524 

1,144 
125 

2,5i  19 

71 

9 

318 

11 

3,142 

295 

9,140 

599 

22.840 

1,347 

33,120 

1.794 
68,096 

8.127 

77.861 
38.58 

22,646 

8,315 

58, 55i  t 


810,320 


684.M25 


-'-      II 


037 
919 


Square  <>t 
Depth  =/*2. 


Ft.* 


1.2 


s 


3, 


h  Net 

Area— z 


T 


■j- 


Sq, 


541 


.65^=  8,„; 


In. 


t\2  Air-. 


Ft/-Sq.In 


7 .  •  >  7  7 
7,359 


Moment  of  Inertia  of  Bj  ctiob  at  Frame  jV. 

Assumed  neutral  axis  =  26..V  above  base. 

Actual  neutral  axis  z=  ifff  =  .65'  below  assumed  neutral   axis  =  25.85' 

above  base  line. 
Moment  of  inertia  about  correct  neutral  axis  =  2  (684,025  +  7,359  —  S06, 

=  1,381,156  Ft.2  Sq.  In. 


184  The  Naval  Constructor 


Curve  of  Load. 

The  curve  of  loads  is  obtained  by  measuring  the  difference 
between  the  curves  of  weight  and  buoyancy  at  the  various  ordi- 
nates  and  spotting  off  the  excess  buoyancy  above  the  base  ;  and  the 
excess  weight  below  their  points  of  intersection  with  this  line  will 
show  the  waterborne  sections,  which  for  calculating  purposes  are 
taken  as  the  points  of  support. 

Curve  of  Shearing  Stresses. 

This  curve  is  calculated  from  the  foregoing  curve  of  load  by 
taking  its  area  at  various  ordinates  measured  from  forward  aft 
and  plotting  these  areas  off  above  or  below  the  base  line  as  in  the 
case  of  the  curve  of  loads,  observing  that  the  greatest  stresses 
will  be  opposite  the  points  of  support  (or  waterborne  sections). 
A  curve  run  through  the  foregoing  spots  will  show  the  shearing 
stresses  graphically. 

Curve  of  Bending  Moments. 

As  the  bending  moment  at  any  section  in  the  length  of  a  ship 
is  equal  to  the  algebraic  sum  of  the  shearing  stresses  in  relation  to 
either  end,  it  is  evident  that  a  curve  of  bending  moments  may  be 
obtained  from  these  stresses  and  plotted  off  as  was  done  for  the 
shearing  curve  from  the  curve  of  loads,  observing  that  the  maxi- 
mum and  minimum  bending  moments  will  be  coincident  with  the 
points  of  support. 

To  apply  similar  curves  and  the  data  constituting  them  to  the 
determination  of  the  stresses  experienced  by  a  ship  amongst 
waves,  it  is  usual  to  take  the  two  extreme  bending  moments  to 
which  a  vessel  is  subjected,  viz.:  (1)  hogging  on  the  crest  of  a 
wave,  and  (2)  sagging  in  the  trough,  and  to  construct  a  trochoid 
wave  of  such  form  as  will  give  the  same  displacement  of  immersed 
body  (in  both  cases)  as  obtained  in  smooth  water.  The  curves 
are  then  calculated  as  explained  in  the  foregoing,  taking  the 
height  of  wave  as  being  Jq  °f  the  length. 

The  subjoined  table  shows  a  specimen  calculation  of  the  moment 
of  inertia  of  the  sections,  observing  that  although  the  rivets  in  this 
case  are  neglected  for  compression,  it  would  probably  be  some- 
what more  accurate  to  include  them. 

Unless  in  exceptional  cases  it  will  be  found  sufficiently  approxi- 
mative for  comparative  purposes  to  multiply  the  displacement  of 
the  proposed  vessel  by  one-thirtieth  to  one  thirty -fifth  of  the  length 
when  the  product  will  equal  the  maximum  bending  moment,  as 


Strength  of  Ships  185 

— - —  =  maximum  bending  moment, 

and  the  minimum  tension  on  sheerstrake  equals 

Maximum  bending   moment  x  Neutral  axis  below  sheerstrake  _ 

Total  moment  of  inertia 

Tension  stress  per  square  inch.  The  compression  on  the  bottom 
plating  is  similarly  computed,  substituting  the  distance  of  neutral 
axis  above  keel  for  "below  sheerstrake.1' 

The  value  of  the  maximum  tensile  strength  per  square  inch  of 
section  varies  of  course  with  the  size  and  proportions  of  vessels. 
A  suitable  value  for  vessels  of  wholesome  proportions  built  to  any 
of  the  great  classification  societies'  rules  is  about  2  tons  per  square 
inch  in  small  vessels  to  about  9  in  the  largest  liners,  taking  the 
comparative  method  of  calculating  the  bending  moment  given 
above. 

It  will  be  evident  from  an  examination  of  the  table  showing  a 
specimen  calculation  of  the  moment  of  inertia  of  a  ship's  cross 
section,  that  the  further  the  sectional  area  of  the  ship  is  arranged 
from  the  neutral  axis,  the  greater  will  be  the  moment  of  resistance 
to  bending.  It  is  in  recognition  of  this  geometrical  quality  that 
the  upper  deck  in  3-deck  and  other  ships  is  made  the  strength 
deck,  and  that  the  keel  plate  and  garboards  are  thickened  as  well 
as  the  sheerstrake  and  stringer  being  increased  at  that  level,  in 
addition  to  reinforcing  the  bilge  ;  for,  with  a  ship  rolling  and 
pitching,  it  must  often  happen  that  the  greatest  bending  moments 
will  frequently  be  exerted  at  the  bilge  and  upper  deck  gunwale. 
By  making  the  shelter  deck  in  3-deck  vessels  the  "strength 
deck,"  a  great  increase  in  the  strength  of  these  ships  has  been  made 
in  recent  years,  as  demonstrated  by  actual  practice,  steamers  of 
this  class  being  now  practically  "4-deckers"  from  a  strength  point 
of  view. 


186  The  Naval  Constructor 

CHAPTER  VIII. 

RESISTANCE  OF  SHIPS. 

The  Admiralty  Coefficient. 

The  amount  of  power  required  to  propel  a  vessel  at  a  given 
speed  is  generally  computed  by  (1)  the  Admiralty  Coefficient  for- 
mula, or  (2)  a  formula  based  on  the  ship's  actual  resistance,  the 
former  being  purely  empirical  and  requiring  great  judgment  and 
practice  in  the  selection  of  the  coefficient,  and  the  other  founded  on 
scientific  experimental  data  and  theories  which  have  acquired  con- 
firmatory proof  amounting  to  law,  since  they  were  first  enunciated 
by  William  Froude.  The  following  notes  on  resistance  are  taken 
principally  from  the  papers  by  this  eminent  investigator,  and  from 
the  later  work  of  Middendorf ,  Taylor,  and  others. 

The  Admiralty  Coefficient  (C)  is  calculated  from  the  results  of 
actual  trials,  and  is  based  on  the  false  assumptions  that  the  area 
of  wetted  surface  (»S)  for  similar  ships  is  proportional  to  the  § 
power  of  the  displacement  (D®),  and  that  the  resistance  (R)  plus 

the  propulsive  coefficient   f    ' '     '      J  varies  as  the  cube  of   the 

speed  (T3).     From  this  we  get  the  well-known  formula  : 

I.H.P.  -u  , 

c 

and  for  the  speed  with  a  stated  I.H.P., 

Cx  I.H.P. 

V3= 1 

Therefore  the  coefficient : 

c_Dix  P~3 
~  I.H.P.  " 

It  will  be  obvious  that  these  coefficients  must  cover  a  wide  range 
of  values,  hence  the  difficulty  of  their  application  by  the  inex- 
perienced. For  this  reason  we  append  a  table  of  values  in  vessels 
of  greatly  divergent  types.  It  should,  however,  be  noted  that  for 
vessels  of  similar  form  but  different  lengths,  the  coefficient  will 
show  great  disparity,  and  for  vessels  of  similar  form  and  length 
but  different  draught,  there  will  likewise  be  much  dissimilarity  in 
the  coefficient.     In  the  selection  of  this  coefficient  it  should  also 


Froude's   Law  of  Comparison  187 

be  remembered  that  the  class  of  steamer  to  which  it  is  applied 
must  be  similar  not  only  in  form,  but  in  type  of  engine  as  well, 
and  of  corresponding  speed.  This  does  not  necessarily  mean  the 
same  speed,  as  will  be  explained  later. 


Table  of  Admiralty  Coefficients. 


Type  of  Vessel. 


Launches  (yachts)     .... 
Launches (navy)       .... 
Vedettes  (high  speed)    .     .     . 
!Speed  launches  and  yachts 
Steam  yachts  (large)      .     .     . 

Torpedo  boats 

Torpedo  boat  destroyers    .     . 

Cruisers 

Harbor  and  revenue  steamers 
River  steamers  (shallow  dr.)  . 
River  steamers  (paddle)  .  . 
River  steamers  (stern  wheel). 
Channel  steamers  .  . 
Freighters  (small)  .  .  .  . 
Freighters  (large)  .  .  .  . 
Intermediate  liners  .  .  .  . 
Ocean  liners 


Length 
L. 


Feet. 
18-30 
27-45 
50-60 
70-100 
1 30-250 
1QO-150 
170-235 
500 
55-75 
00-100 
100-250 
75-150 
250-300 
100-250 
300-500 
500-600 
500-750 


Block 
Coeffi- 
cient, 
8. 


28-.  38 
30-.  40 
35-.42 
41-.43 
40-.48 
40-.  44 
40-.43 

.54 
.45-.  50 
,50-..")  5 
.50-.  60 
.65-.  75 
.58-.  65 
.73-.78 
.78-.78 
.70-.  72 
.60-.  65 


- 


Ad- 
miralty 
Coeffi- 

(  IKNT, 

c. 


Knots 

7  -10 

7  -12 

14  -20 

16  -22 

12  -20 
20  -25 
27  -33 

22 
9  -10 
8J-13 

13  -20 
8|-13 

17  -21 
8J-11 

11  -13 

14  -16 
20  -25 


65-70 

50-70 

75-130 
135-165 
165-175 
140-170 
175-210 

275 
110-120 

85-120 
100-180 

65-120 
240-270 
100-230 
240-280 
270-310 
265-285 


FROUDE'S  LAW  OF  COMPARISON. 

As  the  result  of  experiments  with  models  and  full  sized  ships 
Froude  discovered  that  there  was  great  resemblance  between 
their  "curves  of  resistance,"  i.e.,  a  curve  plotted  off  withascaleof 
knots  as  abscissa,  and  the  poimds  resistance  to  towing  as  ordi- 
nates.     See  Fig.  51. 

To  test  this,  however,  it  is  necessary  to  apply  the  Law  of 
Comparison,  which  he  thus  Btates  :  — . 

"  If  the  ship  be  D  times  the  dimension  of  the  model  and  at  the 
speeds  Vu  V%i  V%  .  •  .  the  measured  resistances  of  the  model 


188 


The  Naval  Constructor 


are  Ei,  R2, -Ks  •  •  .,  then  for  speed  \fSVv    \JDVv    s/DV3  •  •  • 
of  the  ship,  the  resistance  will  be  DBRi,  DSR2,  I>2Rs-  •  •  •" 

To  the  speeds  of  model  and  ship  thus  related,  he  applied  the 
term  "  corresponding  speeds."  This  law  expresses  the  resistance 
due  to  surface  friction,  plus  wavemaking  resistance,  the  former 
being  commonly  referred  to  as  skin  resistance  and  the  other  as 
residuary  resistance,  embracing  as  it  does,  the  resistance  caused 


## 

K^\ 

^/ 

o£> 

20.000 


15,000  ! 


10,000  § 


DC 


5,000 


10  11 

Speed  in  Knots 

Fig.  51. 


12 


13 


by  the  motion  of  the  waves  and  the  drag  of  dead  water  eddies, 
such  as  are  formed  at  abrupt  endings  to  bossings,  the  siding  of 
stern  posts  and  in  the  wake  of  propeller  struts.  The  skin 
resistance  is  proportional  to  the  area  of  wetted  surface,  and  is  re- 
sponsible for  almost  the  total  resistance  up  to  about  8  knots  speed. 
Beyond  this  speed  the  total  resistance  increases  rapidly,  showing 
the  effect  of  the  residuary  resistance.  This  will  be  more  readily 
understood,  when  we  recollect  that  the  wave  undulations  progres- 
sively increase  in  height  with  increases  in  speed,  and  that  the  crests 
of  these  waves  are  accountable  for  about  95  per  cent  of  the  total 
residuary  resistance,  the  remaining  5  per  cent,  as  already  stated, 
being  due  to  eddies,  etc.  Referring  to  the  diagram  here  reproduced, 
showing  curves  of  residuary  and  skin  resistances,  "the  graduated 
undulations  in  the  residuary  resistance  curve  are  due  to  quasi- 
hydrostatic  pressure  against  the  after-body,  corresponding  with 
the  variations  in  its  position  with  reference  to  the  phases  of  the 
train  of  waves  comprising  the  wave  line  profile,  there  being  a  com- 
parative excess  of  pressure  (causing  a  forward  force  or  diminution 


Froude's   Law  of  Comparison 


189 


of  resistance)  when  the  after-body  is  opposite  a  crest,  and  the 
reverse  when  it  is  opposite  a  trough.  Their  spacing  is  uniform 
at  a  uniform  speed,  because  waves  of  given  speed  have  always  the 
same  Length  ;  it  is  more  open  at  the  higher  speeds,  because  waves 
are  longer  the  higher  their  speed;  their  amplitude  is  greater  at 


RESISTANCE  IN  TONS. 


RESISTANCE  IN  TONS. 


RESISTANCE  IN  TONS. 


Fig.  52. 


RESISTANCE  IN  TONS. 


the  higher  speeds,  because  the  waves  made  by  the  ship  are  higher  : 
and  their  amplitude  diminishes  with  increased  length  of  middle 
body,  because  the  wave  system   by    diffusing  itself  transversely 

loses  its  height." 


190  The  Naval  Constructor 

Froude  found  that,  at  the  lower  speeds,  two  ships,  one  200  ft. 
and  the  other  240  ft.  in  length,  had  the  same  residuary  resistance  ; 
the  difference  in  the  larger  vessel  was  simply  due  to  its  increase  of 
skin  friction  due  to  the  greater  wetted  surface.  At  13. 15  knots,  how- 
ever, the  240-foot  vessel  had  the  lesser  total  resistance  of  the  two, 
owing  to  her  position  on  the  residuary  resistance  curve  coming  in 
a  hollow  ;  the  consequent  diminution  in  this  resistance  was  greater 
than  her  increase  of  skin  friction. 

The  resistance  depends  on  the  relative  placing  of  the  after-body 
and  the  wave  system,  and  the  length  spacing  of  the  wave  system 
depends  on  the  speed,  therefore  the  position  of  after-bodies, 
which  is  specially  favorable  at  some  given  speed,  may  be  specially 
unfavorable  at  a  higher  speed,  and  at  a  higher  speed  still  may  be 
favorable  again. 

This  it  is  which  explains  the  economy  with  which  some  vessels 
attain  certain  speed  whilst  others  of  almost  identical  form,  but 
slight  variation  in  length,  fall  short  of  the  others'  performance. 

To  apply  the  investigations  of  Froude  to  actual  ships,  it  is  usual 
to  make  a  model  of  the  proposed  ship  and  run  it  in  a  tank,  and 
from  the  data  obtained  apply  the  law  of  comparison.  For  ex- 
ample, if  a  model  be  made  of  a  liner  700  feet  long  on  a  scale  of 
|  inch  to  the  foot,  and  the  required  speed  of  the  ship  be  24  knots, 
at  what  speed  will  the  model  require  to  be  run  to  correspond  with 
the  desired  velocity  ?  "  In  comparing  similar  ships,  or  ships  with 
models,  the  speed  must  be  proportional  to  the  square  root  of  their 
linear  dimensions."" 

Therefore  the  model  will  be 

700  feet     OIT1  .     , 
-— — —  =  87 h  inches, 
|  inch 

or  7  feet  3|  inches,  and  the  ratio  of  linear  dimensions, 

700  feet     na 

-T29-=96' 
and  speed  corresponding  to  24  knots, 

24  -r  V96  =  2.45  knots. 
In  like  manner,  if  we  are  working  from  the   known  speed  of 
another  ship,  say,  of  600  feet  length,  then : 

£{$  =  1.16  ratio  of  linear  dimensions, 

and  24  -f  ^/lAQ  =  25. 8  knots,    7.  "2. .  3 

corresponding  speed  of  the  600-foot  boat. 

APPLICATION  OF  FROUDE'S  LAW. 

It  is,  however,  in  dealing  with  data  derived  from  trial  perform- 
ances that  the  law  of  comparison  is  invaluable  to  those  having  the 


Application   of  Froude's   Law  191 


responsibility  of  powering  ships.  For,  given  the  trial  data  of  the 
ships,  we  may  apply  this  to  other  vessels  of  similar  form  to  obtain 
the  I.H.P.  necessary  to  drive  them  at  a  stated  speed.  Of  course, 
we  assume  that  the  efficiency  of  the  engines,  boilers  and  propellers 
are  equal  in  both  cases,  otherwise  that  their  coefficients  of  efficiency 
are  the  same.  So  that  when  we  know  the  displacement,  power, 
and  speed  of  a  given  ship  represented  by  D,  P,  and  P,  and  it  is 
required  to  estimate  the  I.H.P.  from  a  proposed  vessel  of  like 
form  of  Di,  Pi,  and  Pi,  then, 


POWER  CURVE 


SFEED  is  KNOT8 

Fig.  53. 


(1) 

and  (2) 

Substituting  values, 

(1) 


(2) 


Pi  = 


Fi  = 


Pi  = 


Pi  = 


:•  29,246 

.000  I.H.P. 


17,878  J 
24  1  knots 


X22.1 


We  may  also  run  a  speed  curve  of  the   known  vessel,  where 
progressive  runs  have  been  made,  as  shown  in  Fig.  53,  and  from 

this  deduce  the  proposed  vessel's  corresponding  curve  with  the  aid 


of  the  formula  given 


192  The  Naval  Constructor 

The  curve  illustrated  is  that  of  a  56-ft.  vedette  pinnace,  and  it  is 
proposed  to  deduce  the  power  curve  of  a  21  knot  speed  launch  from 
it,  being  a  type  of  similar  form. 

Displacement  of  vedette 13.75  tons. 

Displacement  of  speed  launch     .     .     22.50  tons. 

The  corresponding  length  L\  of  the  speed  launch  would  be 
obtained  from  the  length  of  the  vedette  and  the  ratio  of  the  dis- 
placements. 

(^  XL=  (fl^)*  x  56  feet  =  66  feet. 
Corresponding  speed, 

Hg\*    V=(2^fx  19.25=  20.85  knots. 

Corresponding  power, 

m  p=®'*««=«  lh.p. 

So  that  after  the  derived  curve  has  been  plotted  from  the  spots 
calculated  as  above  for  various  speeds,  it  must  be  continued  in  the 
same  contour  until  it  is  opposite  the  21-knot  ordinate,  when  the 
required  power  may  be  read  off. 

STANDARD  CURVES  OF  POWERS. 

Taylor  in  his  "  Resistance  of  Ships  "  advocates  the  adoption  of 
a  "standard"  displacement  in  applying  the  Law  of  Comparison, 
to  which  all  trial  particulars  should  be  reduced,  and  for  this  pur- 
pose takes  10,000  tons  as  a  basis,  giving  tables  of  factors  to 
facilitate  the  reduction  of  the  speed  and  power  data  possessed,  to 
this  standard  displacement. 

He  makes  each  curve  cover  a  range  of  one  knot,  after  the 
manner  shown  on  Fig.  54.  As  an  example  of  the  method 
employed  in  estimating  the  indicated  horse  power  by  the  aid  of 
these  standard  curves  and  tables,  let  us  postulate  that  the  power 
is  required  for  a  proposed  ship  of : 

Length 440  feet. 

Breadth 48  feet. 

Draught 19.5  feet. 

Displacement 7,000  tons. 

Coefficient,  5 .595. 

Speed  18J  knots. 

Then  to  reduce  10,000  tons  displacement,  dimension,  speed,  and 
power  factors  are  calculated. 


Standard  Curves  of  Powers 


193 


In  the  above  case  these  are  1.126,  1.061,  and  1.517  respectively, 

which  work  out  : 

Length    x  1.126  =  495.44  feet. 
Breadth  X  1.126  =  54.04  feet. 
Draught  X  1.126= '-'  1.96  feet. 
Speed      x  1.061=  19.63  knots. 

SPEED  AND  POWER  CURVE 
(STANDARDIZED) 


20,000 
19,000 

18,000 
17,000 

16,000 

■£   15,000 

14,000 

13..000 

s0. 

ii^- 

12,000 

1 1,000 

10,000 

9 

i 

2 

3 

4 

KN 
Fig. 

5 

OTS 
5i. 

a 

7 

3 

9            2 

From  the  diagram  shown  we  find  that  the'  "Umbria"  at  19.63 
knots  took  13,000  I.H. P.  at  10,000  tons  standard  displacement, 
and  this  divided  by  the  power  factor  1.517,  will  give  the  I.H. P. 
required,  viz.: 

1.517 

Any  one  may  prepare  a  set  of  these  standard  curves,  making 
each  one  cover  a  range  of  one  knot,  from  his  own  trial  data. 
These  will  be  found  very    useful,    as  of  the    many    methods 


194  The  Naval  Constructor 


employed  to  estimate  horse  power,  this  is  probably  one  of  the 
most  reliable,  besides  being  easy  of  application.  Of  course,  to  do 
this  one  must  be  possessed  of  the  requisite  data  and  the  judgment 
to  know  how  to  apply  it. 

In  conjunction  with  the  curves,  tables  should  also  be  calculated 
for  the  dimension,  speed,  and  power  factors  for  graduated  dis- 
placements as  follows  : 

The  dimension  factor  is  the  ratio  of  the  linear  dimensions,  as : 

•       e  ,.     ,  10,000      ,   ._ 

Ratio  of  displacement,  =  1.43  ; 

therefore,  dimension  factor 


1=  V  1.43  =1.126 
for  7,000  tons  displacement. 

Speed  factor  =  {j^f=  1.061, 
and  Power  factor  =      '        X  1.001  =  1.517. 

I.H.P.  by  Independent  Method. 

Where  the  type  of  vessel  is  abnormal,  the  speed  excessive,  or 
sufficient  data  to  which  to  apply  the  comparative  method  is  not 
possessed,  the  effective  horse  power  should  be  calculated  in  detail 
from  the  skin  and  wave  resistances,  and  by  the  selection  of  a 
suitable  efficiency  coefficient  for  the  machinery,  the  Indicated 
Horse  Power  may  be  computed  with  great  accuracy.  Por  this 
purpose  it  is  necessary  to  know  the  wetted  surface,  and  this  may 
be  figured  with  the  aid  of  either  of  the  tables  given  on  p.  98. 

The  wetted  surface  determined,  this  area  must  be  multiplied  by 
the  coefficient  of  friction  due  to  the  particular  surface  which  will 
give  the  skin  friction,  and  this  in  turn  multiplied  by  the  power  ne- 
cessary to  overcome  one  pound  resistance  at  one  knot  (.0030707  V) 
by  the  1.83  power  of  the  velocity  required,  will  give  the  E.H.P. 
for  skin  resistance.     Otherwise  stated, 

Skin  resistance  power  =f.S.  . 00307 F283  =  Ea. 
To  this  must  be  added  the  power  for  residuary  or  wave-making 
resistance  Ew. 

Wave  resistance  power  =  .00307  bY5  =  Ew. 

Then  these  two  combined  give  us  the  E.H.P.  for  the  total 
resistance,  from  which  the  I.H.P.  may  be  determined  by  taking  a 
suitable  coefficient  of  efficiency. 

It  should  be  stated  that  "6"  ranges  from  .35  in  swift,  narrow 
vessels,  to  .55  in  full,  slow  vessels. 


Least  Resistance  bv  Middendort's  Method    195 

J 

Substituting  values  and  applying  them  to  the  determination  of 
the  I.H.P.  required  for  the  440-f  t.  steamer  dealt  with  on  p.  189, 
we  have. 

Wetted  surface  =  20,600  sq.  ft.  =  .S. 

Coefficient  of  friction  "/"  =  .009. 

Power  per  pound  of  resistance  at  one  knot  =  .00307  V. 

Percentage  of  efficiency  =60%  of  I.H.P. 

Speed  in  knots  T"  =  18.5. 

Coefficient  b=  .35. 
Then,  Eg  =  .009  x  20. GOO  x  .00307  "T2.83 

=  2.830  E.H.P. 

And,  J?,,  =  . 00307  x.  351" 

=  2,330  E.H.P. 

The  addition  of  the  skin  and  wave  resistance  powers  gives  us 
the  total  effective  horse  power. 

E.H.P.  =  2,830  +  2.330  =  5,100 

and  the  indicated  horse  power  at  60%  efficiency  =  8,600  I.H.P., 
being  a  similar  result  to  that  obtained  by  the  comparative  method. 


Froude's  Frictional  Constants  for  Salt  Water  or 
Smoothly  Painted  Surfaces. 


Length 

COEFFI<TENT 

Length 

Coefficient 

of 

OF 

OF 

OF 

Vessel. 

Fbiction. 

Vessel. 

Friction. 

50 

.00963 

200 

.00902 

60 

.00950 

250 

.00897 

70 

.00940 

300 

.00892 

mi 

.00933 

350 

.00889 

90 

.00928 

400 

.00886 

100 

.00:  »-.•: 

450 

.00883 

120 

.00916 

500 

.00880 

140 

.00911 

550 

.00877 

160 

.00'." '7 

600 

.00874 

180 

.00904 

.  .  . 

.... 

FORM  OF  LEAST  RESISTANCE,  BY 
MIDDENDORF'S  METHOD. 

Herr  Middendorf  gives  the  following  method  of  obtaining  the 
angles  of  entrance  and  run  to  give  the  form  of  least  resistance,  and 


196 


The   Naval   Constructor 


Table  Giving  Angles  of  Entrance  and  Run 

Lengths 


26  Ft. 

40  Ft. 

65  FT. 

90  FT. 

125  FT. 

165  FT. 

TO 

TO 

TO 

TO 

TO 

to 

Speed 

40  Ft. 

65  Ft. 

90  Ft. 

125  Ft. 

165  Ft. 

200  Ft. 

in 
Knots. 

a 
and 

e 

a 
and 

/3 

e 

a 

and 

|3 

0 

a 
and 

e 

a 

and 

/3 

0 

9 

a 
and 

e 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

5 

18.0 

30.5 

18.5 

31.5 

20.0 

33.0 

21.0 

35.0 

22.5 

37.0 

24.0 

39.5 

6 

17.0 

29.0 

17.5 

30.0 

185 

31.5 

20.0 

33.0 

21.5 

35.0 

23.0 

37.5 

7 

16.0 

27.5 

16.5 

28.5 

17.5 

29.5 

18.5 

31.0 

20.0 

33.0 

21.5 

35.0 

8 

15.0 

25.5 

15.5 

26.5 

16.5 

27.5 

17.5 

29.0 

19.0 

31.0 

20.0 

33.0 

9 

14.5 

24.0 

14.5 

25.0 

15.5 

2G.0 

1G.5 

27.5 

17.5 

29.0 

18.5 

30.5 

10 

13.5 

22.5 

14.0 

23.0 

14.5 

24.0 

15.5 

25.5 

16.5 

27.0 

17.5 

28.5 

11 

12.5 

21.0 

13.0 

21.5 

13.5 

22.0 

14.5 

23.5 

15.0 

25.0 

16.0 

26.5 

12 

11.5 

19.5 

12.0 

20.0 

12.5 

20.5 

13.0 

21.5 

14.0 

23.0 

15.0 

24.5 

13 

10.5 

18.0 

11.0 

18.5 

11.5 

19.0 

12.0 

20.0 

13.0 

21.0 

13.5 

22.5 

14 

10.0 

16.5 

10.5 

17.0 

10.5 

17.5 

11.0 

18.5 

12.0 

19.5 

12.5 

21.0 

15 

9.0 

15.5 

9.5 

16.0 

10.0 

16.5 

10.5 

17.0 

11.0 

18.0 

11.5 

19.0 

16 

8.5 

14.5 

8.5 

14.5 

9.0 

15.0 

9.5 

16.0 

10.0 

16.5 

10.5 

17.5 

17 

8.0 

13.5 

8.0 

13.5 

8.5 

14.0 

9.0 

14.5 

9.0 

15.5 

9.5 

16.5 

18 

7.5 

12.5 

7.5 

12.5 

7.5 

13.0 

8.0 

13.5 

8.5 

14.5 

9.0 

15.0 

19 

7.0 

11.5 

7.0 

12.0 

7.0 

12.5 

7.5 

13.0 

8.0 

13.5 

8.5 

14.0 

20 

6.5 

11.0 

6.5 

11.0 

7.0 

11.5 

7.0 

12.0 

7.5 

12.5 

8.0 

13.0 

21 

6.0 

10.5 

6.5 

11.0 

6.5 

10.5 

7.0 

11.5 

7.5 

12.0 

22 

6.0 

10.5 

6.0 

10.5 

6  5 

11.0 

7.0 

11.5 

23 
24 
25 
26 

6.0 

10.0 

6.0 
6.0 

10.5 
10.0 

6.5 
6.0 
6.0 

10.5 

10.0 

9.5 

Angles  of  Entrance  and   Run 


197 


for  Ships  of  Various  Lengths  and  Speeds. 

in  Ftet. 


200  Ft. 

260  Ft.       320  Ft. 

390  Ft. 

460  FT. 

540  Ft. 

620  FT. 

to 

to               to 

TO 

to    • 

to 

I.. 

260  Ft. 

320  Ft. 

390  Ft. 

460  Ft. 

540  FT. 

620  Ft. 

720  Ft. 

a 
and 

0 

a 

and 
0 

9 

a 

and 

0 

9 

a 

ami 
0 

9 

a 

and 
0 

9 
5 

a 

and 

0 

o 

9 

a 

and 

0 

9 

0 

o 

o 

o 

o 

0 

o 

o 

o 

o 

o 

o 

26.0 
24.5 
23.0 
21.5 

42.0 
39.5 
37.0 
35.0 

27.5 
26.5 

44.5 
42.0 

28.0 
26.5 
25.0 

44.5 
42.0 
39.5 

24.5    39  5 

28.0 
26.5 

44.5 
41.5 

23.0 

37.0 

28.f) 

44.0 

20.0 

32.5 

21.5 

34.5 

23.0 

36.5 

24.5 

39.0 

26.5 

41.0 

28.5 

44.0 

19.0 

30.5 

20.0 

32.0 

21.5 

34.0 

23.0 

36.0 

24.5 

38.5 

26.5 

41.0 

28.5 

44.0 

it.:. 

28.0 

18*5 

30.0 

20.0 

32.0 

21.5 

34.0 

23.0 

36.0 

25.0 

38.0 

26.5 

41.0 

16.0 

26.0 

17.0 

27.5 

18.5 

29.5 

20.0 

31.5 

21.5 

33.5 

23.0 

35.5 

25.0 

38.0 

14.;. 

24.0 

15.5 

25.5 

17.0 

27.5 

18.5 

29.0 

20.0 

31.0 

21.5 

33.0 

23.0 

35.0 

13.5 

22.0 

14.5 

23.5 

15.5 

25.0 

17.0 

27.0 

18.5 

28.5 

20.0 

30.5 

21.0 

32.5 

12.5 

20.0 

13.0 

21.5 

14.5 

23.0 

15.5 

25.0 

17.0 

26.5 

18.0 

28.0 

19.5 

30.0 

11.5 

19.0 

12.0 

20.0 

13.0 

21.5 

14.0 

23.0 

15.5 

24.5 

16.5 

26.0 

18.0 

27.5 

io.r. 

17.5 

11.0 

18.5 

12.0 

19.5 

13.0 

L'1.0 

14.0 

22.5 

15.0 

23.5 

16.5 

25.0 

9.5 

16.0 

10.0 

17.0 

11.0 

18.0 

12.0 

19.5 

13.0 

20.5 

13.5 

21.5 

1.-..0 

'_"_'. 5 

9.0 

14.5 

9.5 

15.5 

10.0 

16.5 

11.0 

17.5 

11.5 

18.5 

12.5 

19.5 

13.5 

20.5 

8.0 

13.5 

8.5 

14.5 

9.0 

15.0 

10.0 

16.0 

10.5 

17.0 

11.0 

17..-. 

12.0 

18.5 

7.5 

12.5 

8.0 

13.0 

8.5 

13.5 

9.0 

14.5 

9.5 

15.0 

10.0 

16.0 

11.0 

16.5 

7.0 

11.5 

7.5 

12.0 

8.0 

12  5 

8.5 

13.0 

9.0 

13.5 

9.5 

14.0 

9.5 

15.0 

6.5 

11.0 

7.0    11  5 

7.5 

1 1 .:. 

7.5 

12.0 

8.0 

12.5 

8.5 

13.0 

8.0 

13.5 

G.O 

10.0 

6.5     10.5 

7.0 

io.r. 

7.0 

11.0 

7.5 

11.0 

7.5 

1 1 ..". 

9.0 

12.0 

6.0 

9.0 

6.0    mo 

6.0 

10.0 

6.0 

10.0 

6  5 

10.5 

7.0 

10.5 

7.0 

11.0 

6.0 

9.0 

6.0      9.0 

6.0 

10.0 

6.0 

10.0 

6.0 

in.:. 

G.r. 

10.5 

7.0 

io.r. 

198 


The  Naval   Constructor 


u 
o 
z 
< 

H 
CO 

CO 
UJ 

cc 

h- 

co 
< 

UJ 

_l 

LL 

o 

cc 

o 

LL 


Form   oi   Least   Resistance  199 


appended  is  a  table  giving  the  value  of  these  angles  for  various 
speeds  and  lengths  of  vessels  obtained  from  actual  well-known 
ships  of  the  best  form. 

On  the  construction  lines  of  the  body  plan  and  profile,  a  mean 
water  line  is  drawn  half  way  between  keel  and  load  line,  as  shown 

D 
at  2' 

By  referring  to  the  table  of  angles,  a  is  selected  for  the  length 
of  vessel  being  designed  and  the  tangent  of  the  same  spotted  on 
the  half-breadth  plan.  This  will  give  the  outline  of  the  mean 
water  plane. 

Two  diagonals,  D  and  Dx,  are  struck  in  on  the  after  body  plan, 
the  former  intersecting  the  centre  line  at  half  the  draught,  as  well 
as  the  base  line  at  a  distance  equal  to  the  half-breadth  of  the  ship, 
and  Di  intersecting  the  load  water  plane  at  centre  line  as  well 
as  the  half  moulded  breadth  construction  line  at  the  mean  water 
line  height,  as  shown  in  Fig.  55. 

The  angles  £  and  6  are  obtained  from  the  table  and  transferred 
to  the  half-breadth  plan  representing  the  half  planes  of  B  and  D\ 
respectively. 


200 


The  Naval  Constructor 


ELEMENTS    OF 


Moulded 

H 

fc 

.    "* 

6  • 

0<d 

Dimensions. 

fa 
63 

3  b 

*2   ~ 

-    H 

O    „ 

Name. 

Description. 

A 

43 

A 

+9 

< 
A 

>A  fa 

O    *H 

a2 

1»S 

be 

ci 

+3 

3 

fa 

—  — 

03  fn 

a  fa 

a 

<v 

A 

c3 

05 

cq  fa 

£  fa 

-  fa 

/ 

u 

pq 

0) 

ft 

u 

ft 

i— i 

fa 

fa  a 
On 

gw 

Campania  . 

1st  Class  Ocean 

/    // 

/ 

// 

Liner,  T.S.     .     . 

600 

65  0 

41    6 

2610 

19,336 

.644 

.667 

.976 

Manchuria 

1st  Class  Interme- 

diate Liner,  T.S. 

600 

65  0 

43   3 

33 

2 

26,514 

.715 

.762 

.942 

Norrnannia 

1st  Class  Ocean 

Liner,  T.S.     .    . 

500 

57  3 

38   0 

24 

0 

11,588 

.59 

.625 

.94 

Tantallon 

1st    Class    Cape 

Castle 

Liner      .... 

440 

50  5 

3411 

24 

6 

10,100 

.647 

.695 

.932 

Kiev  .    .    . 

Russian  Volunteer 

419 

49  6 

32   0 

2311 

10,640 

.738 

.769 

.959 

Texan    .    . 

1st  Class  Ocean 

Freighter,  T.S.  . 

471 

57  0 

35   0 

27 

0 

16,236 

.784 

.820 

.958 

Nevadan    . 

1st  Class  Ocean 

Freighter,  T.S.  . 

360 

46  0 

27    2 

23 

0 

8,217 

.758 

.788 

.961 

M.  S.  Dol- 

Ocean  Freighter, 

S.S 

300 

40  0 

26   0 

22 

0 

5,960 

.79 

.801 

.986 

Victoria 

Channel,  T.S.    .     . 

220 

28  0 

17    0 

10 

0 

860 

.502 

.569 

.822 

Jupiter  .     . 

Sound,  P.S.  .    .    . 

230 

28  0 

9    6 

6 

7i 

699 

.578 

.621 

.930 

Greyhound 
Tynwald*  . 

Channel,  P.S.    .     . 

'>30 
265 

27  0 
34  4 

10   0 
14    6 

610i 
10   0 

690 
1,508 

.568 
.58 

.622 
.594 

.913 
.976 

Channel,  T.S.    .'    . 

Sandy  Hook 

260 

37  0 

15    0 

10 

2 

1,165 

.417 

.5 

.82 

Mayflower . 

Yacht,  T.S.   .     .     . 

275 

36  6 

21    0 

15 

G 

2,414 

.535 

.612 

.874 

Giralda  .     . 

Yacht,  T.S.   .     .     . 

275 

35  0 

19    0 

13 

6 

1,862 

.505 

.498 

.904 

Ophelie*     . 

Yacht,  Auxiliary 

Composite      .    . 

160 

26  6 

17   0 

11 

6 

568 

.407 

.59 

.682 

Lady  Tor- 

Yacht,  Auxiliary 

frida* .    . 

Steel 

157 

27  0 

17   0 

11 

6 

552 

.3968 

.6 

.664 

Zaida*    .    . 

Yacht,  T.S.    .    .    . 

136| 

22  6 

13    9 

8 

9 

332 

.428 

.59 

.73 

Pizzaro  .     . 

Guard  Boat,  S.S.  . 

155 

21  6 

11    0 

6 

6i 

303 

.482 

.626 

.773 

Ponce  de 

Leon   .    . 

Guard  Boat,  S.S.  . 

135 

19  0 

10    6 

6 

6J 

202 

.439 

.594 

.74 

Sandoval    . 

Guard  Boat,  S.S.  . 

110 

15  6 

8   9 

5 

0 

100 

.407 

.610 

.667 

Fradera*     . 

Guard  Boat,  S.S.  . 

74 

11  9 

7    3 

4 

0 

41 

.412 

.662 

.622 

Scud*     .     . 

Speed  Launch,  S.S. 

86 

10  7 

5  10 

2 

9 

30 

.43 

.625 

.687 

Neuquen* . 

Revenue  Steamer, 

S.S 

65 

12  0 

7    0 

4 

3 

4H 

.437 

.585 

.757 

Princess 

Customs  Launch, 

Maud*     . 

S.S 

12  0 

6    8    • 

6 

37 

.435 

.56 

.776 

*  Designed  by  the  Author. 


Elements   of  Typical   Steamers 


201 


TYPICAL    STEAMERS. 


-  .- 

-  ~ 

—     — 
•- 

.726 

- 

C 

.47(1.' 

■/. 

—  y. 
Y.  z 

<r* 

-  •-' 

■  ~      — 
^     _ 

Y. 

■V 

.1821) 

■r. 
y 

z 

D 

- 

Y 

— 

c 

y.  y. 

K  c 

<  < 
£  y. 

17,878 

— 

y.  — 

-  - 

is 

11  - 

7!) 

■/'. 
H 
C 
y. 

M 
ft" 

- 

en 

-  y. 

**  < 

—  r 
~  1 

-.' 
<^> 

252 

7,610 

2,960 

1H.570 

.6531 

t 

4,665 

29,246 

22.09 

.82G 

7,987 

.474 

1,844 

.1092 

9.831 

.583 

2,100 

.  .  . 

12,000 

7.", 

14 

.718 

4,525 

.416 

1,677 

.154 

6,202 

.57 

2,526 

10,535 

16,300 

94 

20.75 

263 

.777 
.837 

7.101 
9,065 

8,379 
3,844 

79 
98 

17.23 
13.93 

227 
306 

2,827 

.426 

1,167 

.1758 

3,995 

.6019 

627 

.875 

3,891 

.463 

637 

.0704 

4.528 

.539 

731 

8,390 

3,535 

7.", 

12.8 

245 

.847 

2,125 

.472 

531 

.118 

2.656 

.59 

528 

.  .  . 

3,000 

75 

.868 

1,210 

.388 

328 

.105 

1 .5.38 

.493 

447 

2,522 

1,302 

88 

11.25 

207 

.607 

272 

.26 

172 

.1641 

444 

.424 

203 

736 

1,400 

201 

16.5 

260 

.693 

196 

.320 

98 

.1602 

394 

.48 

221 

550 

2,421 

56 

18.18 

116 

.698 

195 

.314 

88.5 

.1425 

283.5 

.4565 

195.5 

524 

2.022 

58 

18.49 

203 

.07 

446 

.338 

236 

.179 

682 

.517 

590 

1,130 
2,365 

5,200 
2,800 
4,604 

161 
128 

107 

18.92 

17.0 

16.36 

•    •    • 

190 
169 

.721 

994 

.1716 

672 

.3186 

1,666 

.7902 

484 

.668 

700 

.3823 

347 

.1895 

1,047 

5718 

500 

1,661 

7,223 

218 

20.64 

172 

.692 

115 

.164 

221 

.3150 

336 

.4790 

83 

532 

646 

110 

11.73 

164 

.656 

200 

.277.', 

140 

.1945 

340 

.4720 

85 

598 

720 

134 

11.62 

155 

132 

.312 

7»i 

.1653 

202 

.4773 

92 

353 

620 

150 

12.8 

169 

.684 

91 

.248 

39 

.1073 

130 

.3555 

55 

257 

504 

242 

13.4 

193 

59 

.2193 

37 

.136 

96 

.3554 

38 

107 

338 

270 

13.14 

203 

.666 

31 

..joss 

24 

.1618 

55 

.3706 

29 

101 

229 

294 

12.09 

167 

.67 

14 

.219 

8 

.125 

22 

.344 

81 

41 

180 

295 

11.5 

100 

.686 

9 

.17 

4.4 

.083 

13.4 

.253 

14.0 

31i 

531 

430 

20.34 

155 

.695 

12 

.22 

5 

092 

17 

.312 

12.5 

39J 

97 

318 

10.1 

119 

1.68 

16 

.364 

4.5 

.](r2 

20.5 

.400 

10.5 

37 

81 

228 

9.27 

108 

Section  II. 

STRENGTH   OF   MATERIALS. 


CHAPTER   I. 
STRESSES. 

It  is  by  the  application  of  the  known  strengths,  as  derived  by 
experiment,  of  the  various  materials  used  in  shipbuilding  to  the 
physical  properties  possessed  by  their  geometrical  sections  that  we 
are  enabled  to  calculate  with  accuracy  the  loads  they  will  bear 
with  a  predetermined  margin  of  safety  when  subjected  to  either 
of  the  four  simple  stresses  of  tension,  compression,  shearing  and 
torsion. 

Ultimate  Strength  is  the  direct  stress  producing  rupture  of 
the  material. 

Working  Load  is  the  stress  applied  in  practice,  and  its  ratio  to 
the  ultimate  .strength  varies  with  the  nature  of  the  stresses  applied, 
viz.:  (1)  tension  with  a  dead  load;  (2)  tension  with  a  live  load, 
or  (3)  a  live  load  working  alternately  in  opposite  directions  (see 
Table). 

Many  of  the  fittings  in  shipwork  come  under  the  third  category, 
as  in  rudders,  derricks,  etc.  In  derricks  the  inertia  of  the  load 
has  not  only  to  be  overcome,  but  also  the  jarring  and  surging.  For 
this  reason  a  very  common  factor  of  safety  for  these  details  is  ten 
times  the  ultimate  strength. 


•»' 


Proof  Strength  is  the  test  load  to  which  cranes,  davits,  der- 
ricks, chains,  cables,  etc.  are  subjected,  and  is  usually  a  multiple 
of  the  working  load  or  ultimate  strength.  Careful  measurements 
should  be  taken  before  applying  this  load,  and  these  checked  after 
the  load  has  been  removed,  to  discover,  if  any,  the  amount  of 
permanent  set. 

Stress  and  Strain. —  Stress  is  the  measure  of  the  internal  force 
or  resistance  in  a  bar  due  to  the  load  applied  tending  to  produce 

203 


204  The  Naval  Constructor 

deformation,  and  strain  is  the  alteration  of  form  due  to  the  stress. 
So  that  the  relationship  between  these  two  terms  really  is  one  of 
cause  and  effect,  although  in  general  the  terms  are  erroneously 
used  synonymously. 

Stress  is  measured  by  weight  and  strain  in  inches,  or  as  a  per- 
centage of  the  length  of  the  bar  or  member  strained.  Thus,  we 
say  that  a  5-foot  bar  is  subjected  to  a  tensile  stress  of  20  tons,  pro- 
ducing a  strain  of  |  inch  per  foot  (elongation  being  §  inch)  or  1.04 
per  cent  of  the  bar's  length. 

Tensile  Stress.  — If  two  equal  forces  acting  in  opposite  direc- 
tions, away  from  each  other,  be  applied  to  a  bar,  they  will  tend 
to  stretch  it,  thus  producing  a  tensile  strain. 

Compressive  Stress. —  Should,  however,  the  forces  act 
towards  one  another  they  will  produce  a  compressive  strain. 

Shearing  Stress.  — When  two  forces  acting  in  opposite  direc- 
tions are  exerted  through  the  cross  section  of  a  pin  or  rivet  con- 
necting two  flat  bars,  the  pin  is  subjected  to  single  shear.  If, 
however,  another  similar  bar  be  connected  enclosing  either  of 
the  other  bars,  then  the  pin  or  rivet  will  be  in  double  shear,  and 
may  be  reduced  by  half  its  original  sectional  area. 

Bending  or  Transverse  Stress.  —  Bending  stresses  are  im- 
posed on  beams  when  they  are  loaded  or  forces  exerted  on  them, 
although  more  correctly,  tensile,  compressive  and  shearing  stresses 
are  at  work  simultaneously  on  the  top,  bottom  and  abutments 
respectively. 

Torsional  Stress  is  encountered  mostly  in  shafting  and  in  the 
rudder  stocks  of  ships.  In  the  latter  case  it  consists  of  twisting 
stresses  acting  alternately  in  opposite  directions,  requiring  a  much 
larger  margin  of  safety  than  necessary  with  any  of  the  other 
stresses  named. 

Resilience.  — This  term  is  applied  to  the  amount  of  work  done 
by  compressing  or  extending  a  bar  and  multiplying  the  length  of 
such  compression  or  extension  by  the  load  which  produced  it. 

Elasticity  is  the  property  which  substances  possess  of  return- 
ing to  their  original  size  and  shape  after  straining.  In  tension 
materials  increase  in  length  and  decrease  Under  compressive 
stresses,  and  within  certain  limits  this  lengthening  or  shortening 
is  proportional  to  the  stress  applied.  From  this  it  is  evident 
that  this  quality  is  more  important  than  even  the  strength  of  the 
material  in  tension  or  compression. 

Modulus  of  Elasticity.  —  The  amount  of  this  proportional 
variation  of  the  weight  applied  and  the  alteration  in  length  of  the 


Stresses 


205 


bar  is  known  as  the  modulus  of  elasticity,  and  may  also  be  expressed 
as  the  tensile  force,  which,  when  applied,  will  double  the  bar's 
length,  and  of  course  may  be  different  in  the  same  material  when 
subjected  to  tension,  compression  or  shear. 

Permanent  Set.  —  If  a  bar  be  extended  or  contracted  by  the 
application  of  a  load  beyond  its  elastic  limit,  it  is  said  to  have 
permanent  set.  This  would  take  place  in  mild  steel  if  a  load  of 
17  tons  per  scpiare  inch  of  section  were  exceeded. 


LOAD 


Fig. 

56. 

Distance*. 

Ak  i:  \ . 

Moments. 

Si     = 

4.40 

X 

2.04 

=      80.40 

S2     = 

1.75 

X 

1.48 

4.73 

>.     = 

2.00 

X 

1.64 

=       6.56 

s4    = 

8.75 

X 

2.44 

=      84.80 

Moment  of  Inertia  / 
Section  Modulus       Z 


85.08 
5: 15 


85.08 
=  16.5. 


The  Moment  of  Inertia  of  a  section  or  body  is  a  mathematical 
quantity  used  to  calculate  the  strength  of  materials,  and  is  taken 
relatively  to  the  neutral  axis  or  centre  of  gravity  of  the  section. 
If  the  section  of  a  bulb  tee  beam,  as  shown  in  Fig.  66,  be  cen- 
trally loaded  on  top,  the  fibres  above  the  line  xy  (neutral  axis)  will* 
be  compressed,  and  those  below  extended,  and  consequently  the 
arc  formed  by  the  table  of  the  beam  will  be  shorter,  and  that 
formed  by  the  bulb  longer,  than  the  arc  through  the  line  NS, 


206  The  Naval  Constructor 

which  will  be  exactly  the  same  length  as  the  original  dimension 
of  the  beam  before  the  application  of  the  load,  the  laminse 
through  this  axis  being  neither  in  compression  nor  tension,  and 
are  therefore  known  as  the  neutral  surface  of  the  beam.  Hence, 
if  we  take  very  small  areas  at  known  distances  from  the  neutral 
axis  to  their  centres  of  gravity  and  multiply  these  areas  by  the 
square  of  their  distances  above  or  below  this  line,  we  shall  have 
by  adding  the  products  together  the  moments  of  inertia  (I)  of  the 
section  ;  and  again  by  dividing  this  moment  by  the  distance  of  the 
most  extreme  fibre  we  shall  get  the  quantity  known  as  the  section 
modulus. 

In  the  example  given  the  result  is  fairly  accurate,  although  a 
more  absolute  result  may  be  obtained  by  greater  subdivision  of 
the  areas.  This,  however,  is  not  necessary  for  ordinary  calcula- 
tions. 

The  value  of  the  section  modulus  depends  entirely  on  the  geo- 
metrical form  of  the  section.  The  material  of  which  the  beam  is 
made  and  its  ultimate  strength  known  and  divided  by  the  factor 
of  safety  selected,  gives  us  the  safe  limiting  stress.  This  stress 
multiplied  by  the  section  modulus  produces  the  moment  of  resis- 
tance of  the  beam.  In  the  example  given  let  the  beam  be  of  steel 
of  60,000  lbs.  ultimate  strength  and  the  factor  of  safety  5,  we 
then  have  £2400  _  12,000  lbs.  safe  limiting  stress,  and  section 
modulus  =  16.5  X  12,000  lbs.  =  198,000  lbs.  moment  of  resistance. 
Suppose  then  that  this  were  a  12-foot  boat  skid  beam  fixed  at 
both  ends  and  loaded  at  centre,  what  weight  of  steam  pinnace 
would  it  safely  support  ?  The  maximum  bending  moment  on  a 
beam  so  loaded  would  be  |  WL  where  W  is  the  weight  and  L  the 
length  between  points  of  support.  Equating  this  bending  moment 
with  the  moment  of  resistance,  we  have 

SZ      WL 

X--8-' 
then  ir  =  11,000  lbs. 

Where  the  figure  or  section  is  symmetrical  about  its  centre  of 
gravity  the  /  and  other  elements  may  be  readily  figured  from  the 
appended  Table  of  Elements  of  Usual  Sections. 

Radius  of  Gyration.  —  The  radius  of  gyration  is  that  funda- 
mental property  of  a  section  used  in  determining  the  strength  of 
pillars  and  struts,  and  its  square  or  rz  about  a  given  axis  is  equal 
to  the  moment  of  inertia  of  the  surface  about  the  axis  divided  by 
the  area,  therefore  the  radius  of  gyration 


\     are 


tia 
ea 


Stresses 


207 


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208 


The   Naval   Constructor 


ELEMENTS    OF    SECTIONS. 


Section. 


-D-+i 


-b-J 


y^b 


Moment  of 

Inertia. 


0.0491  (D*-d*) 


Alfi 


10 


0.1098r4 


0.7854  6a* 


A4 
12 


B*-b* 


12 


36 


Resistance. 


0.0982 


D*-d* 


AD 


8 


V,\=  0.1098r3 
Wr2=  0.2587  r* 


0.7854  6a2 


6/i2 


0.1178  #» 


1F-64 


6      i>' 


6^2 
24 


Base 

FBOM 

C.G. 


D 
2 


D 

3~ 


0.4244 r 


h 
2 


2? 

2" 


Least  Ra 
dius  OF 

GVKATION 


y(D^-d^ 


D 

1 


0.0699  r2 


Least  side 


\h 


3.46 


3T46 


./£2+62 
V"~12~ 


The  lesser, 

h  6 

or  — 

4.24       4.9 


Figs.  57  to  64. 


Elements  of  Sections 


209 


ELEMENTS    OF    SECTIONS.  —  (Continued.) 


Section. 


Moment  <>k 
Inertia. 


6  frH-ti  &&!+&!* 


RE8I8Q  \  N I  I : : . 


*&fc     ~~Wz 


n 


1 

i 


•Wj-S 


r 

6 

-N 

1 

' 1 

l(—h 


30  (2  6 +  6^ 


AJfi 


Ir 


-~-l< 


r> f 


--—6- 


ai 


-tj — H 


9.9 


Ah2 

Kt.4 


^l/<2 


19 


Ah2 

ToT9 


0.1 


Ah' 
6.73 


6&H-66&rW 


^ 


Bask 

FROM 

<■.<;. 


I  36+6! 


I.r  L8T  IIa- 
DIl'S  OF 

Gyration. 


12(3  6  +  2  6!)  "  3  26  +  6i 


Ah 
0.7 


Ah 


7.4 


4A 
•   9.5 


Ah 


.6 


::.n 


.!// 

;;.;; 


h 
3~T 


3.5 


2 


3.3 


2 


A 

2 


fl6 


2.6(A  +  6) 


5 


4.74 


4.00 


b_ 
6.2 


3.50 


Figs.  t£  to  71. 


210 


The  Naval  Constructor 


BEAM    BENDING    MOMENTS.  ETC. 


■W=LOAD.       L=LENGTH  OF  BEAM  BETWEEN  SUPPORTS.       K  — FIBRE  STRESS. 
l=-MOMENT  OF  INERTIA.       E^MODULUS  OF  ELASTICITY.       R=^=  RESISTING  MOMENT 
C  —DISTANCE  OF  EXTREME  FIBRES  FROM  NEUTRAL  AXIS. 


HOW  LOADED  &  SUPPORTED 


STRESS  DIAGRAM 
ORDINATES  GIVE  BENDING  MOMENTS 


Draw  ED=wl  &  AF=^ 


Draw  DA  =^-p 


Figs.  72  to  83. 


Beam    Bending   Moments 


211 


BEAM    BENDING    MOMENTS,    ETC. 


K  =  Fibre  Stress 


L  =  Length  <>t  lieain  between  Supports. 
1  =  Moment  uf  Inertia. 

E  :=  Modulus  of  Elasticity.    R=,     =  Resisting  Moment. 
C  =:  Distance  of  Extreme  Fibresfrom  Neutral  .\\i~. 


Bbkdikg 

Mom  em  r,  Jf. 


.1/=   H 

.1/ .  xx  =  jrz^ 


.1/"= 


.l/nwj  


2 

u/. 


For  AD,M= 


Wdxx 


For  BD,M=U'f'1 


-'/  max  — 


ir,/</, 


Fur  .//>. 
For  J!  I  >. 

Md=f,  WL 


2     \Z       V 


.'/    HOC   


irz 


For  .4  and  Z^, 


DEFLECTION,  ./'. 


II' 


/. 


y—    3      £/ 


f-  *L  IL 

J        48     El 


>"^i 


^Sd{dx-\-L) 


J  ~  768  El 

_Viv  PZ3 

J  max  —  V  _  X  

5      48E1 
For 

.'  =zVr 


/= 


ILIL 

192  £  I 


J  '       16     I.I 


Kim  MOM 

\r  A  and  /;. 
9afe  Load  H 


z?  =  »r 


A  —  B  — 


W 


ir  =  * 


KB 


_  HV, 


Z^  = 


IIV 


I/" 


KJi 


ddx 


BliABTK    «   i   i:\  r. 
EQC  \  I  TON. 


y  = 


»'Z3 
2  El 


[—       1  —  1 

[z       3  Z3  J 


JFL3 
16  EI 


Vx       4  x3~l 
I  Z  ~~  3  Z3J 


:  6Z/.7 

I  2   '  ■    I   gt         J-3    1 
L"  rf  ^  </,       dn-  </,  I 

Jf'(/-(/,2 


#1= 


6  LEI 


4= 


fa 


FF 


5  =  is  ir 


w  = 


16  AT? 
3   Z/ 


'=■»=■? 


jr  =  8 


A/.' 


.=,= : 


W—2 


Kll 


y  — 

W  U  fx      5  j»l 

32  £V  LZ       3  Z3  I 

-  'L' Ji 
'/l_  32  /;/ x 

Uz^o  Z2     3   Z3J 


y  = 


16  EI 


X 


Lz2      3  Z     I 


y—f— p+ 


v„«_. 


.77 


H*(--f) 


117 


=Constant 


212 


The  Naval  Constructor 

BEAM    BENDING    MOMENTS,  ETC. 


W=LOAD.       L"=LENGTH  OF  BEAM  BETWEEN  SUPPORTS.       K=FIBRE  STRESS. 
I      MOMENT  OF  INERTIA.       E  =  M0DULU8  OF  ELASTICITY.       R=-g— RESISTING  MOMENT 
C—DISTANCE  OF  EXTREME  FIBRES  FROM  NEUTRAL  AXIS. 


4 


V^^lfll 


igQ_OG)L6QQOOp 

lh„...    »_WL   B.  or-      WL       m 


|jDraw  A=^L  &  BC-* 


§• 


W 


Draw  Parabola  BC=^ 


f"°°ooooOQOQ 
L 


h~«4 


Figs.  84  to  95. 


Beam    Bending   Moments 


213 


BEAM    BENDING    MOMENTS,    ETC.  —  (Continw  d  ) 
PF=Load.  L 

E  =  Modulus  of  Elasticity. 


Length  of  Beam  between  Supports. 

/ 


11  =r      =  Resisting  Moment 


A"  =  Fihre  Stress.    -                     /=  Moment  of  Inertia. 
C  =  Distance  of  Extreme  Fibres  from  Neutral  Axis. 

1'.  i  nimn<; 
.M.»  ,i  i:\  i .  .1/. 

Dbfijeo- 

TluN,  /. 

lii:  \i  Tn  ».\  .\  r 

.1    AM)    A'. 

Safk  Load,  If. 

Elastic  Cthyk 
Equation. 

i/  - "c 

.IJ  maz  —  — ^— 

•          8     A7 

r=2™ 

7- 

A'  =  W 

'/  — 

24    El 

V I  -  $} 

w  u 

"  =  24    El  X 

r,        or'        r4-| 

I  /.       "  A^Z,*J 

v      -  WL 

.1.  maz  —  — g — 

O 

5  PFZ» 

•  ~~  384  a:/ 

M        -  WL 

.11  max  —  — ~ — 
Q 

M,  —   l     WL 
128 

l'jj  A  7 

Max.  deflec- 
tion, 
x  =  0.4215  A 

ii  =  8  W 

w  =  sKTR 

W    L* 

V  —  48   A  / 

[z-»S+»S] 

2    \6      L^LV 

M        -   WL 

.*!  max  —  — — r~ 

WL* 

J  ~ 384  A/ 

W  =  12  V'' 

1j 

ir/,3 

y=24£7 

I  /.-       A'  +  A4  | 

-*/  //iaJT  — — — ' 

O 

•'  '"  15  A 7 

b  —  ir 

W=3%> 

Lt 

117.' 

'  =  12*2 

V  r         1    /  " 
|  /.  ~  5  A •• 

Rx=A(a+£w) 

.       W(2d 

A=         ll. 
B_W(2aJrb) 
2  A 

214  The   Naval   Constructor 

USE    OF    THE    TABLE    OF    ELEMENTS    OF 
CIRCULAR    SECTIONS. 

In  calculating  the  scantlings  of  masts,  derricks,  kingposts,  rud- 
ders, shafting,  and  details  generally,  where  circular  sections  are 
employed,  the  Table  of  Elements  will  be  found  very  convenient 
and  time-saving,  as,  having  determined  on  a  thickness  or  a  diam- 
eter to  which  it  is  decided  to  work,  the  appropriate  formulae  for 
the  various  elements  may  be  read  off  with  facility. 

In  the  first  column  is  given  the  ratio  of  internal  to  external  di- 
ameter. It  is  required  to  find  the  elements  of  a  hollow  section 
with  an  outside  diameter  D  =  5  inches  and  an  internal  diameter 
d  =  .8D  =  4  inches,  or  5"  x  \"  thick. 

Column  2  gives  the  sectional  area  coefficient  of  the  pipe,  viz., 
.2826  XL?  =7. 065  square  inches. 

Similarly  the  coefficient  for  the  moment  of  inertia,  J,  is  found 
in  the  third  column  to  be  .02899  by  the  fourth  power  of  the  diam- 
eter D,  or  .  02899  X  625  =  18. 1 18  =  I. 

By  the  fourth  column  we  get  the  coefficient  for  the  square  of 
the  least  radius  of  gyration  as  .1026  D2  =  .1026  x  25  =  2.565, 
and  in  the  following  or  fifth  column  the  radius  of  gyration  =  .32 
D  =  .32  x  5"  =  1.6. 

For  the  moment  of  resistance  of  the  section,  or  I/y,the  coefficient 
for  the  pipe  with  a  ratio  of  .8  D  is 

.05798  2)8  =  .05798  X  125  =  7.247. 

The  torsional  moment  of  resistance  is 

.11595  I)3  =  .11595  x  125  =  14.493. 

If  it  be  required  to  select  a  diameter  of  hollow  or  solid  circular 
section  for  a  given  moment  of  inertia,  or,  having  obtained  a  diam- 
eter, it  is  found  advisable  to  amend  the  same  to  another  diameter 
giving  the  same  J,  then  the  increase  or  decrease  of  thickness  may 
be  readily  computed  with  the  aid  of  column  8,  and  in  a  like  man- 
ner the  sectional  area  for  a  constant  moment  of  inertia  is  calcu- 
lated by  the  coefficients  in  the  following  column. 

The  last  two  columns  give,  similarly,  the  diameters  and  areas 
for  a  constant  moment  of  resistance. 

Inversely  we  may  calculate  the  diameter  of  a  bar  or  tube  equal 
to  a  given  moment  of  inertia,  or  moment  of  resistance,  or  radius 
of  gyration,  etc.  For  example,  the  diameter  is  required  of  a  tubu- 
lar section  which  shall  equal  a  moment  of  inertia  of  12.  It  is 
proposed  to  make  the  pipe  relatively  thin  ;  therefore  we  select  a 
ratio  of  d/D  =  .90  per  column  one,  from  which  we  get  an  I  co- 
efficient =  .01689  ;  therefore, 

D={/3I=V4/^:=^710 
V  .01689      V  .01689 
=  5. 14  inches  outside  diameter  x  \  inch  thick  (fully). 


Elements   of  Circular  Sections 


215 


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21G 


The   Naval   Constructor 


MOMENT    OF   INERTIA   OF    CIRCULAR    SECTIONS. 


If) 

INERTIA  OF   CIRCULAR   SECTIONS. 

t       7)      i' 

=  Mom.  of  Inertia.    Z—  Moment  of  Resistance. 

1        V        1 

nil 

nrf3 

nd* 

„      nd6 

,     irrf* 

~    *ds 

D 

Z— 

D 

z—-^ 

D 

1—-7TT 

z=^r 

1 

~64 

32 

34 

~  64" 

32 

67 

64 

32 

0.0491 

0.0982 

65,597 

3,859 

989,166 

29,527 

2 

0.7854 

0.7854 

35 

73,662 

4,209 

68 

1,049,556 

30,869 

.3 

3.976 

2.651 

36 

82,448 

4,580 

69 

1,112,660 

32,251 

4 

12.57 

6.283 

37 

91,998 

4,973 

70 

1,178,588 

33,674 

5 

30.68 

12.27 

38 

102,354 

5.387 

71 

1,247,303 

35,138 

G 

63.62 

21.21 

39 

113,561 

5,824 

72 

1,319,167 

36,644 

7 

117.9 

33.67 

40 

125,664 

6,283 

73 

1,393,995 

38,192 

8 

201.1 

50.27 

41 

138,709 

6.766 

74 

1,471,963 

39,783 

9 

322.1 

71.57 

42 

152,745 

7,274 

75 

1,553,156 

41,417 

10 

490.9 

98.17 

43 

167,820 

7,806 

76 

1,637,662 

43,096 

11 

718.7 

130.7 

44 

183,984 

8,363 

77 

1,725,571 

44,820 

12 

1,018 

169.6 

45 

201,289 

8,946 

78 

1,816,972 

46.589 

13 

1,402 

215.7 

46 

219,787 

9,556 

79 

1,911,967 

48,404 

14 

1,886 

269.4 

47 

239,531 

10,193 

80 

2,010,619 

50,265 

15 

2,485 

331.3 

48 

260,576 

10,857 

81. 

2,113,051 

52,174 

16 

3,217 

402.1 

49 

282,979 

11,550 

82 

2,219,347 

54,130 

17 

4,100 

482.3 

50 

306,796 

12,272 

83! 

2,329,605 

56,135 

18 

5,153 

572.6 

51 

332,086 

13,023 

84! 

2,443,920 

58.189 

19 

6,397 

673.4 

52 

358,908 

13,804 

85! 

2,562,392 

60,292 

20 

7,854 

785.4 

53 

387,323 

14,616 

86 

2,685,120 

62,445 

21 

9,547 

909.2 

54 

417,393 

15,459 

87! 

2,812,205 

64,648 

22 

11,499 

1,045 

55 

449,180 

16,334 

88! 

2,943,748 

66,903 

23 

13,737 

1,194 

56 

482,750 

17,241 

89, 

5,079,853 

69,210 

24 

16,286 

1,357 

57 

518,166 

18,181 

90, 

3,220,623 

71,569 

25 

19,175 

1,534 

58 

555,497 

19,155 

91 

3,366,165 

73,982 

26 

22,432 

1,726 

59 

594,810 

20,163 

92, 

3,516,586 

76,448 

27 

26,087 

1,932 

60 

636,172 

21,206 

93 

3,671,992 

78,968 

28 

30,172 

2,155 

61 

679,651 

22,284 

94 

3,832,492 

81,542 

29 

34,719 

2,394 

62 

725,332 

23,398 

95, 

3,998,198 

84,173 

30 

39,761 

2,651 

63 

773,272 

24,548 

96' 

1,169,220 

86,859 

31 

45,333 

2,925 

64 

823,550 

25,736 

97- 

1,345,671 

89,601 

32 

51,472 

3,217 

65 

876,240 

26,961 

98' 

1,527,664 

92,401 

33 

58,214 

3,528 

66 

931,420 

28,225 

99- 
100' 

1,715,315 

1,908,738 

95,259 
98,175 

7T  :  64  =  0.0490874  ;  log  (n  :  64)  =  0.6909699  —  2. 
n  :  32  =  0.0981748  ;  log  (tt  :  32)  =  0.9919999  —  2. 


Strength   of  Columns  21 


CHAPTER    II. 

STRENGTH    OF    COLUMNS. 

John  son 'a  Formi  la. 

The  accompanying  table  of  strengths  of  wrought  iron  columns  is 
based  on  the  "straight  Line  *'  formula  proposed  by  Johnson  and  gen- 
erally used  in  America.  The  value  of  the  constant  K  is  deduced 
by  making  the  straight  line  tangent  to  the  curve  of  Eider's  for- 
mula. 

r 

"Where.  P  =  Ultimate  unit  stress. 

>  =  Maximum  compressive  unit  str<  ss. 

k  —  A  constant  whose  value  depends  on  the  condition 

of  the  ends,  viz.,  fixed,  flat,  hinged  or  round. 
L  =  Length  of  column  in  fe» 
r  =  Least  radius  of  gyration. 

This  formula  may  be  readily  memorized  for  wrought  iron  col- 
umns, thus  :  — 

Ultimate  unit  stress  P  =  52,500  —  2700     •   on   which  basis   the 

table  has  been  calculated. 

Example.  —  It  is  required  to  find  the  safe  load  with  a  factor  of 
safety  of  5  for  a  hollow  wrougbt-iron  strut  or  column  with  a  length 
of  46  feet,  mean  diameter  20  inches  and  one-half  inch  thick. 

r  =  20  x  .35=  7. 

L      46  ._ 

—  =  —  =.  6.57. 

r 

P  (from  table)  =  6,900  lbs. 
Area  of  column  — circ.  x  £  =  62.8  >  .5  =  31.4  □" 
-  ife  Load  11'  =  6.000  lbs.  x  31.40  D"  =216,660  lbs. 
Or,  if  it  be  required  to  find  the  thickness  t  of  the  column  in  the 
foregoing  example,  the  load  being  216,660  lbs. 

r  =  7. 

=  6. 57 
r 

p  =  6,900  lbs.  (from  table). 


218 


The   Naval   Constructor 


216,660      ~  A  „„ 

Araa=-po<r=31-4n  " 

Area     81.4       „  .     , 
t  =  ^r. —  =  t^-^  =  .5  inch. 


Circ.      62.8 
Values  of  r  for  various  sections. 


When 


t- 


t  = 


Fig.  96. 


D 

TO' 
D 

8' 
D 

D 


r=  .32  D. 
r=  .3131). 
r=  .301  D. 
r=  .279  D. 


(See  Table  of  Elements  of  Circular  Sections.) 


Fig.  97. 


1° 


Fig.  98. 


L 


-p- 


Fig.  99. 


Least  radius  of  gyration  = 


D 


Rectangle  or  square  r  =  .289  D. 


Equal  sided  angle  bar  r  = 


D 


J 


L 

Fig.  100. 

T"T 
D 


D 


t^        i- 


Fig.  ioi. 


r=z  A  D. 


r  = 


D 
B. 


Strength   of  Columns 


219 


VALUES   FOR    JOHNSON'S    FORMULA. 


Colt. mx  Material 

jj 

axd 
How  Supported. 

S. 

k. 

Limit  of  — , 

Mild  steel  : 

Flat  ends     .... 

52.500 

2,148 

16.3 

Hinged  ends     .     .     . 

52,500 

2,640 

13.3 

Round  ends     .     .     . 

52,500 

3,408 

10.3 

Wrought  Iron : 

Flat  ends     .... 

42,000 

1,536 

18.2 

Hinged  ends     .     . 

42.000 

1,884 

14.8 

Round  ends      .     .     . 

42.000 

2,436 

11.5 

Cast  Iron : 

Flat  ends     .... 

80.000 

5,256 

10.2 

Hinged  ends     .     .     . 

80.000 

6,44  4 

8.3 

Round  ends      .     .     . 

80.000 

8,316 

6.4 

Oak : 

Flat  ends     .... 

5,400 

336 

10.7 

• 

220 


The   Naval   Constructor 


STRENGTH    OF   WROUGHT   IRON    OR   MILD 
STEEL  COLUMNS. 

Bv  Johnson's  Formula. 


L   in  Ft. 

52,500  —  2,700- 

13,125—675- 

10,500  —  540- 

8,750  —  450  - 

r    in  I n . 

r 

r 

r 

r 

L 

Ultimate 

Unit  Stress 

Safe 
Unit  Stress 

Safe 
Unit  Stress 

Safe 
Unit  Stress 

1 

\_/    i  i   '   '        y^s  k.1  '    V-'k^O  * 

Factor  =  4. 

Factor  =  5. 

Factor  =  6. 

1.00 

49,800 

12,450 

9,960 

8,300 

1.25 

49,125 

12,281 

9,825 

8,187 

1.50 

48,450 

12,112 

9,690 

8,075 

1.75 

47,775 

11,944 

9,555 

7,963 

2.00 

47,100 

11,775 

9,420 

7,850 

2.25 

46,425 

11.606 

9,285 

7,737 

2.50 

45,750 

11,437 

9,150 

7,625 

2.75 

45,075 

11,269 

9,015 

7,513 

300 

44,400 

11,000 

8,880 

7,400 

3  25 

43,725 

10,931 

8,745 

7,287 

3.50 

43,050 

10,762 

8,610 

7,175 

3.75 

42,375 

10,594 

8,475 

7,063 

4.00 

41,700 

10,425 

8,340 

6,950 

4.25 

41,025 

10,256 

8,205 

6,837 

4.50 

40,350 

10,087 

8,070 

6,725 

4.75 

39,675 

9,919 

7,935 

6,612 

5.00 

39,000 

9,750 

7,800 

6,500 

5.25 

38,325 

9,581 

7,665 

6,387 

5.50 

37,650 

9,412 

7,530 

6,275 

5.75 

36,975 

9,244 

7,395 

6,162 

6.00 

36,300 

9,075 

7,260 

6,050 

6.25 

35,625 

8,906 

7,125 

5,937 

6.50 

34,950 

8,737 

6,990 

5,825 

6.75 

34,275 

8,569 

6,855 

5,712 

7.00 

33,600 

8,400 

6,720 

5,600 

7.25 

32,925 

8,231 

6,585 

5,487 

7.50 

32,250 

8,062 

6,450 

5,375 

7.75 

31,575 

7,894 

6,315 

5,262 

8.00 

30,900 

7,725 

6,180 

5,150 

8.25 

30,225 

7,556 

6,045 

5,037 

8.50 

29,550 

7,387 

5,910 

4,925 

8.75 

28,875 

7,219 

5,775 

4,812 

9.00 

28,200 

7,050 

5,640 

4,700 

9.25 

27.525 

6,881 

5,505 

4,587 

9.50 

26.850 

6,712 

5,370 

4,475 

9.75 

26,175 

6,544 

5,235 

4,362 

Strength   of  Columns 


221 


STRENGTH    OF    WROUGHT  IRON    OR  MILD 

STEEL    COLUMNS.  —  Continued. 

By  Johnson's  Fobmui  v. 


/  in  Ft. 

r  in  In. 

/. 

52,500—2,700 

/ 

13,125  —  675 

r 

10,500-    540 

8,750-  460 

r 

r 

Safe 

Safe 

Safe 

I. 

Ultimate 

Unit  St • 

I'nit  Stress 

Unit  Stress 

r 

Unit  Stress. 

tor  =  4. 

F  ustor  =  5. 

Factor  =  6. 

10.  MO 

25,500 

6,375 

5,100 

4,250 

10.25 

2  4.^2.". 

6,206 

1,966 

4,137 

10.60 

24.150 

6,037 

4,830 

4,025 

10.75 

2::.  4  7.-, 

5,869 

4,696 

3.912 

11.00 

22.800 

5.700 

4.560 

3.8O0 

11.25 

22,125 

5.531 

4,425 

3,6^7 

11.50 

21.450 

5,362 

4,290 

3,575 

11.75 

2<i.775 

5.104 

4.135 

3,4«',2 

12.00 

20,100 

5.025 

4.O20 

3.850 

12.25 

10.425 

4.^56 

8.885 

3.287 

12.50 

1-.750 

4,687 

3,750 

3,125 

12.75 

18.<>7.-. 

4.519 

3,615 

3,012 

13.00 

17.400 

4,350 

3, 4  SO 

2.000 

13.25 

16.725 

4.181 

8.845 

2.787 

13  50 

10.050 

4.012 

3,210 

2.0,75 

18.75 

15.375 

3.844 

8.075 

2.562 

14.00 

14,700 

3.675 

2.040 

2.450 

14.26 

14,025 

3,506 

2.805 

2.837 

14.60 

13,350 

8.887 

L'.070 

2,225 

14.75 

12.075 

3.10*.' 

J.535 

2.112 

15.00 

12. 000 

3,000 

2.400 

I'.'lOO 

I-"..  25 

11.825 

2.831 

2.265 

1,887 

15.50 

10,650 

2,662 

2,130 

1, 775 

15.75 

0.07.-. 

2.404 

1,905 

1,662 

16.00 

9,300 

2.325 

1,860 

1.550 

i»;  25 

s.i  ;•_':, 

2.181 

1.72.'. 

1,437 

16.50 

7.050 

1,987 

1,590 

1,325 

16.75 

7.275 

1.81'.' 

1,455 

1.212 

17.00 

500 

1,650 

1.320 

1,100 

17.25 

5,95 

1,481 

1,185 

987 

17.50 

-"..L'50 

1,312 

1,050 

87:. 

17.75 

4,575 

1,144 

915 

70.2 

18.00 

3,900 

075 

7-i 

650 

18.  2  5 

3,225 

806 

•  15 

537 

18.50 

2,550 

•     - 

425 

18.75 

1,875 

469 

375 

312 

222 


The  Naval  Constructor 


PIPE   PILLARS. 


Radii  of 

Gyration  \ 

V#2  +  d*. 

H  7a 

Thickness  in  Decimals  of  an 

Inch. 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

lln. 

2" 

.67 

1 

.64 

.61 

.58 

.56 

.54 

.52 

.51 

.50 

.50 

3 

1.03 

.99 

.96 

.93 

.90 

.88 

.85 

.83 

.81 

.79 

4 

1.38 

1.35 

1.31 

1.28 

1.25 

1.22 

1.19 

1.16 

1.14 

1.12 

5 

1.73 

1.70 

1.66 

1.63 

1.60 

1  .57 

1.54 

1.51 

1.48 

1.46 

6 

2.08 

2.05 

2.02 

1.98 

1.95 

1.92 

1.89 

1.86 

1.83 

1.80 

7 

2.43 

2.40 

2.36 

2.33 

2.30 

2.27 

2.24 

2.21 

2.18 

2.15 

8 

2.79 

2.76 

2.72 

2.69 

2.66 

2.62 

2.59 

2.56 

2.53 

2.50 

9 

3.15 

3.11 

3.08 

3.04 

3.01 

2.97 

2.94 

2.91 

2.88 

2.85 

10 

3.51 

3.47 

3.4.4 

3.40 

3.37 

3.33 

3.30 

3.27 

3.23 

3.20 

11 

3.86 

3.82 

3.79 

3.75 

3.72 

3.68 

3.65 

3.62 

3.58 

3.55 

12 

4.21 

4.18 

4.15 

4.11 

4.08 

4.04 

4.01 

3.97 

3.94 

3.90 

Standard   Pipe   Elements 


223 


STANDARD    PIPE    ELEMENTS. 


STANDARD  STRENGTH 

PIP]  3. 

i. 

z  - 
—  >; 

--7. 

>. 

\\ 

r      Pi 

»  -  " 

O      < 

■  <   • 
ft  »  < 

~~  ~  - 

.:  -  M 

—> 

-  - 
fc  - 

i. 

—  -.   H 

Kr-i  — 
I  LN<  E, 

/ 

Y' 

Kaixi 

•  \     i.VKA- 

TION,   /.'-• 

-  Z  A 

■- '. 

.405 

.27 

.0573 

.0717 

.0010:;-.' 

.005195 

.014808 

.241 

\ 

.54 

.304 

.1041 

.1249 

.003312 

.01- 

.026508 

.42 

1 

.675 

.404 

.1917 

.1663 

.007267 

.02153 

.043716 

.559 

\ 

.84 

.623 

.3048 

.2402 

.017045 

.04058 

.068358 

.837 

5 

1.05 

.824 

.5333 

..3327 

'  .037035 

.07054 

.111342 

1.115 

1 

1.315 

1.048 

.4954 

.10665 

.1622 

.1176721 

1.668 

U 

1.66 

1.38 

1.496 

.668 

.1047 

.2345 

.29125 

2.244 

u 

1.0 

1.611 

2.038 

.707 

.3091 

.32.-4 

.46283 

8^.678 

2 

2.375 

2.067 

3.356 

1.074 

.666 

.5609 

.61957 

4.608 

2* 

-  375 

2.468 

4.784 

1.708 

1.532 

1.0657 

729 

5.739 

3 

3.5 

3.067 

7.388 

2.243 

3.023 

1.7274 

1.3533 

7.536 

3i 

4 

3.548 

9.887 

2.679 

4.788 

2.304 

1.7868 

0.001 

4 

4.:. 

4.026 

12.73 

3.174 

7.23 

3.213 

2.2787 

10.66 

4 

5 

4.508 

15.96 

3.674 

10.41 

4.164 

2.8326 

12.34 

5 

5.563 

5.045 

19.99 

4.316 

15.21 

5.468 

3.52 

14.50 

6 

6.625 

6.065 

2^.89 

-  584 

28.17 

8.504 

5.0422 

18.76 

I 

" 

7.023 

.  38.74 

6.926 

46.5 

12.197 

6.7165 

23.27 

8 

8.625 

7.982 

50.04 

8.386 

72  35 

16.777 

8.6114 

28  18 

9 

9.625 

8.937 

_  73 

10.03 

108.2 

22.483 

10.782 

33.70 

10 

10.75 

10.019 

78  -4 

11.9-2 

160.9 

29.935 

13.40<5 

4"  06 

11 

12 

1 1 .25 

99.40 

13.70 

231.7 

38.617 

16 

45.95 

12 

\ 

12 

113.1 

14.58 

42X765 

10.160 

48.98 

13 

14 

13.25 

137.9 

16.05 

373 

53.28 

23.222 

53. 

14 

15 

14.25 

159.5 

17.23 

461 

61.467 

26.504 

57.89 

15 

M 

15.25 

182.1 

18.41 

70.25 

30.535 

61.77 

224 


The   Naval   Constructor 


STANDARD 

PIPE 

ELEMENTS.  —  {Continued.) 

ft 

EC  t;  H 
O      <5 

05  ft  H 

fc      S 

■  <  • 
**< 

i— i 

O  J 
H  w 

W  fa  H 
O      H 

Resis- 
tance, 
I 

r" 

fa     *• 

K  «  - 

a  ©  s*< 

—  r£  ^ 

£  F vJ 

8 

.405 

.205 

.033 

.036 

.001234 

.00609 

.01288 

.29 

1 

.54 

.294 

.068 

.161 

.003807 

.01410 

.02363 

.54 

I 

.675 

.425 

.139 

.219 

.008588 

.02545 

.03977 

.74 

1 
5 

.84 

.542 

.231 

.323 

.020204 

.04811 

.06246 

1.09 

1 

1.05 

.736 

.452 

.414 

.045261 

.08621 

.10276 

1.39 

1 

1.315 

.951 

.71 

.648 

.10665 

.16220 

.16466 

2.17 

6 

S 

li 

1.66 

1.272 

1.271 

.893 

.2442 

.27012 

.27329 

3 

H 

1* 

1.9 

1.494 

1.753 

1.082 

.3952 

.41631 

.36513 

3.63 

< 

H 
X 

2 

2.375 

1.933 

2.935 

1.495 

.8767 

.73827 

.58607 

5.02 

2$ 

2.875 

2.315 

4.209 

2.283 

1.9434 

1.3522 

.85155 

7.67 

3 

3.5 

2.892 

6.569 

3.052 

3.932 

2.2771 

1.2884 

10.25 

3i 

4 

3.358 

8.856 

3.71 

6.325 

3.1625 

1.7048 

12.47 

4 

4.5 

3.818 

11.449 

4.445 

9.72 

4.3200 

2.1767 

14.97 

5 

5.563 

4.813 

18.19 

6.12 

20.67 

7.4312 

3.38 

20.34 

6 

6.625 

5.75 

25.97 

8.505 

40.93 

12.356 

4.8096 

28.58 

i 

.84 

.244 

.047 

.507 

.024266 

.05777 

.04782 

1.7 

3 

1.05 

.422 

.139 

.727 

.058098 

.11066 

.08004 

2.44 

& 
O 

1 

1.315 

.587 

.271 

1.087 

.14097 

.2144 

.12961 

3.65 

H 

1.66 

.885 

.615 

1.549 

.3426 

.4128 

.22115 

5.2 

H 

1* 

1.9 

1.088 

.93 

1.905 

.57092 

.6010 

.29961 

6.4 

2 

2.375 

1.491 

1.744 

2.686 

1.3194 

1.1117 

.49148 

9.02 

H 

XI 

w 

2£ 

2.875 

1.755 

2.419 

4.073 

2.8873 

2.0085 

.70910 

13.68 

3 

3.5 

2.284 

4.097 

5.524 

6.030 

3.4457 

1.0916 

18.56 

1-3 
« 
p 
o 

3J 

4 

2.716 

5.794 

6.772 

9.895 

4.9475 

1.4610 

22.75 

4 

4.5 

3.136 

7.724 

8.18 

15.38 

6.8355 

1.8803 

27.48 

5 

5.563 

4.063 

12.965 

11.34 

33.63 

12.0906 

2.9636 

38.12 

6 

6.625 

4.875 

18.666 

15.896 

66.87 

20.1872 

4.2285 

53.11 

Steel    Columns 


225 


STEEL    COLUMNS. 


/ 

Lehtgtb  in  Feet. 

Size  of 
Colim.v. 

Z    f 

— — 

Y,  . 

:  t 

2          4          6 

8 

10 

12 

14 

16 

18 

Greatest  Safe  Load  in  Pounds  per  Sq.  In.  of  Section. 

12  ins.     ( 
diameter,! 
g"  thick,  *j 
R  =  4.03.   1 

Fixed 
Flat 
Hinged 
Hound 

23,000  23,000 
23,000  23,000 
23,000  23,000 

23,000  23,000 

1 
23,000 
23,000 
23,000 

23,000 

I 
20.920  17,050  15,570  14.6.UJ  14,030 
20,920  17,050  15.570  14,630  14,030 
20,140  16,390  14,810  13,8lo  13,090 
18,760  15,260  13,670  12,450  11,590 

13,590 
13,590 
12,580 
10,880 

10  ins.     f 

diameter,! 
A"  thick,  "] 
A  =  3.37.  ^ 

Fixed 
Flat 
Hinged 
Round 

23,000  23,000 
23,000  23,000 
23,000  23,000 

23,000  23,000 

22,810 
22,810 

22,030 
20,950 

17,780  15.570  14,500, 13,870  13,26o' 12,500 
17,780  15,570  14.500  13,870 \\.  .200  12,5(0 
17.040  14,830  13,660  12,880  12,260  11,460 
15,780  13,690  12,280  11,340  10,470    9,580 

8  ins.     f 
diameter.! 
.'."  thick.  1 
"A  =  2.66.   i. 

Fixed 
Flat 
Hinged 
Round 

23,000  23,000 
23,000  23.000 
23,000  23,000 
23,000  23,000 

18,600 
18,600 
17,850 
16,480 

15,490  14,250  13.550  12.570  ll,69o'l0.900 
15,490  14,250  13,550  12,570  11,690  10.900 
14,740  13,350  12.540  11,560  10.630    9,670 
13,590  11,910  10,820    9,690    8,620    7,650 

6  ins.     f 
diameter, , 
3    thick,  ' 
A  =  2.00. 

Fixed 
Flat 
Hinged 
Round 

23,000  20,770 
23,000  20,770 
23,000  19,990 
23,000  18,650 

15  2310 
15,510 
14,760 
13,610 

14.000  12.870  11.70010,670 
14,000  12,870  11.700  10. 660 
'13,060  11,880  10.650    9,390 
11,540  10,040    8,640   7,350 

9.7201  8,980 
9,670    8,730 
8,190    7,200 
6,110    5,140 

5  ins.     f  Fixed 
diameter,  ,    Flat 

thick,  "    Hinged 
A=  1.64.   ^  Bound 

23,000  17,350  14,370 
23,000  17,350  14,370 
23,000  16,630  13,500 
23,000  15,430  12,090 

13,060  11.600  10,360    9,280 
13,060  11.600  10.340    9,180 
12,080  10.520    9.000    7,620 
10,270    8,500    6,940    5,550 

8,500    72590 
8,070    7,050 
6,550   5.550 
42510,  3,560 

4  ins.     f  Fixed 
diameter,  ,   Flat 
¥'  thick,  1    Hinged 
A  =  1.33.  1  Round 

23  .Of tO  15,490  13.550 
23,000  15,490  13,550 
23,000  14.740  12.54H 
23,000  13,590  10.820 

11.690  10.170    8,970    7,940 

11,690  10,140    8,710    7,420 

10,630    8.760    7.180   5,920 

8,610,  6,680    5,120    3,900 

6,830   5,910 
6,220   5.120 
4,710    3,560 
2,850    2,040 

3  ins.      r 
diameter,! 
;'/'  thick. 
H—  1.00.   1. 

Fixed 
Flat 
Hinged 
Round 

20.770  14.000  11.700 
20,770  14.000  11.700 
19,990  13,060  10,650 

18.650  11,540    8.640 

9.720    8.350    6.850    5.590 
9,670    7,850    6,250    4.790 
8,190    6,350    4.740    i 
6,110    4,310    2,860    1,88 

4.2S0   3.300 
3,560    2,790 
2,230    1,620 

1 .270       910 

2  ins.     ( 
diameter, 
\"  thick,  ' 

A=0.' 

Fixed 

Flat 

Hinged 

Round 

15,450  11,640    8.920 
15,45o  11.040    8,650 
14,700  10,570    7,120 
13,530    8,560    5,060 

6,780    4.810    3.238    2.290 
6.150    4.( 'in    2,730    2,020 
4,(40    2,580    1,580    1,090 
2,790    1.510       890       630 

1.760   ... 
1,450   .  .  . 

790   ..  . 

450    ..  . 

226 


The   Naval   Constructor 


STEEL   COLUMNS.  —  Continued. 


Size  of 
Column. 


12  ins.     f 
diameter,! 
§"  thick,   1 
A!  =  4.03.   t 

10  ins.     f 
diameter,! 
£"  thick,  ) 
It  =  3.37.  I 


8  ins. 
diameter, 
£"  thick, 
y?=2.66. 

6  ins. 
diameter, 
f"  thick, 
R  =  2.00. 

5  ins. 
diameter, 
£"  thick, " 
i2=1.64. 

4  ins. 
diameter, 
i"  thick,  ' 
R=  1.33. 


3  ins.      r 
diameter,! 
ft"  thick,  j 

#  =  l.oo.  l 


Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Hound 


Fixed 
Flat 
Hinged 
Round 


Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 


Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 


2  ins.      f    Fixed 


Length  in  Feet. 


20 


22 


24        26 


28 


30 


32 


34 


36 


Greatest  Safe  Load  in  Pounds  per  Sq.  In.  of  Section. 


12,930  12,350 
12,930  12,350 


diameter, 
i"  thick, 
It  =  0.66. 


Flat 

Hinged 

Round 


11,940 
10,110 

11,770 

11,770 

10,730 

8,720 

10,170 

10,130 

8,760 

6,680 

8,350 
7,850 
6,350 
4,310 

6,730 
6,100 
4,580 
2,750 

4,880 
4,100 
2,620 
1,540 

2,650 

2,280 

1,250 

720 


11,310 

9,400 

11,150 

11,150 

9,990 

7,960 

9,460 
9,410 
7,870 
5,790 

7,570 
7,030 
5,530 
3,540 

5,990 
5,200 
3,630 
2,080 

4,000 
3,310 
2,050 
1,150 

2,100 

1,860 

1,000 

580 


11,750 

11,750 

10,700 

8,690 

10,550 
10,540 

9,230 
7,180 

8,970 
8,710 
7,180 
5,120 

6,850 
6,250 
4,740 
2,860 

5,160 
4,370 
2,860 
1,670 

3,280 

2,760 

1,610 

910 

1,800 

1,490 

810 

460 


11,230 

11,230 

10,080 

8,070 

9,980 
9,950 
8,520 
6,450 

8,490 
8,050 
6,540 
4,500 

6,250 
5,500 
3,940 
2,300 

4,350 
3,630 

2,280 
1,300 

2,790 

2,380 

1,320 

760 


10,730 

10,710 

9,450 

7,410 

9,430 
9,370 

7,830 
5,750 

7,940 
7,420 
5,920 
3,900 

5,590 
4,790 
3,250 
1,880 

3,720 
3,100 
1,880 
1,050 

2,330 

2,050 

1,110 

650 


10,240 

10,220 

8,850 

6,770 

9,040 
8,830 
7,300 
5,230 

7,350 
6,810 
5,310 
3,340 

4,910 
4,120 
2,640 
1,550 

3,180 

2,700 

1,550 

870 

2,010 

1,760 

940 

550 


9,770 
9,730 
8,260 
6,180 

8,670 
8,090 
6,770 
4,730 

6,830 
6,220 
4,710 
2,850 

4,280 
3,560 
2,230 
1,270 

2,800 

2,390 

1,320 

760 

1,790 

1,480 

800 

460 


9,340 
9,260 
7,710 
5,630 

8,280 
7,780 
6,270 
4,240 

6,380 
5,660 
4,110 
2,420 

3,760 
3,130 
1,910 
1,060 

2,430 

2,120 

1,160 

670 


9,020 
8,800 
7,260 
5,200 

7,820 
7,290 
5,790 
3,780 

5,910 
5,120 
3,560 
2,040 

3,300 

2,780 

1,620 

910 

2,110 

1,870 

1,000 

590 


Strength   of  Metals  and  Alloys  227 


STRENGTH    OF    METALS    AND    ALLOYS. 
S  trt  i  se&  given  in  Pounds  j»  r  Squart  Inch.) 


Ml  i  w.. 


Aluminium  Bronze: 
10     Al,  90%  Cu  (rolled) 

v     Cu(cast) 
Bra^s  and  Bronze  : 

Cupper  Tin     Zinc 


-  ©    ■ 

3  2  c 

-  -^  ._ 

-  -  B 
- 


- 


-  —  ■ 

-  _  - 

—  —  r 

-  A  — 

I—     ~-  S 

-  " 


85 
90 

:<•". 
on 
-I, 

7U 
00 
50 

>o 

70 
60 

55 


1". 

10 

5 


12 
10 
10 


K> 
20 
30 

4n 
50 
2 
20 
30 
44i 


(  <lun- 


Bli'Uze,  Manganese  (<-;i>t 
"  ••  i  n.lled i 

Phosphor  .     . 
"        Tobiu  (rolled) 
Copper  (cast)      .     .     . 
(sheet)    .     .     . 
wire  annealed  . 
Iron  Cast  (average) 
••     Wire  annealed     . 
••     hard  drawn 
••     Wrgt.,  rolled  bars 
"    plates 

Le  id 

-   1  (mild)  .... 

Tin 

Zinc  (cast)  .... 


100,000 
26,800 


35. 500 
33,000 
30,000 
30,000 
37,000 
43,000 
49,000 
24,000 
34,600 
31,760 
21,500 

0.\! 

71.200 
100,000 
47. Too 
70.400 
24.80O 
32,600 
39,800 
17.000 
45.000 
75,000 

50, I 

50,000 

2,050 

67,200 

3,500 

5.4oo 


-  £ 


.'-  z 

J   ■- 

m  — 


f.   - 
—•   — 

S3 


-  '-■-  "Z  -"_ 

_  —  _  *^  -   - 

O 


75.000 
62,000 
48,000 
65,000 

70.000 

75.000 

117,400 


oo. 18.0 


03,000 
52,000 
39,000 
24,000 
30,000 
36,000 
42.000 
48.000 
62,400 
43,500 
30,200 


2O.0HO   .  .  . 

.   .   .    14  0 

16,00013.7 


130.000 


10.000  12.4 

9,100  14.o 

16,4oo  12.2 

10,900  11.6 

12.5 

14.5 

15.8 


175.000  41,900 


22.000  .  .  . 
17.700  .  .  . 

80. 000 1  .  .  . 
21.500  .  .  . 
55,400  .  .  . 

8,000  18.0 


100,000 


30.000 
7.350 
6,400 


25,000  18.0 
6,000  15.0 


27,000  26.0 
30,000  29.0 
30,000  29.0 

1.100    0.85 
35,00029.00 
1,670   4.6 
4,050  .  .  . 


2^2 


319 
318 
317 
.322 
,316 
,310 
,308 
304 
315 


■_«..,; 


26 


228  The   Naval   Constructor 


PHYSICAL   PROPERTIES   OF   TIMBER. 

The  physical  properties  of  timber,  given  hereafter,  are  derived 
largely  from  the  recent  experiments  of  the  Forestry  Division, 
United.  States  Department  of  Agriculture,  which  form  the  most 
complete  and  systematic  series  on  record.  The  following  general 
conclusions  seem  to  be  demonstrated  : 

1  That  bleeding  (the  experiments  were  made  on  long-leaf  yel- 
low pine)  has  no  material  effect  on  the  strength  of  timber,  the 
flexibility  is  slightly  increased,  but  the  bled  timber  will  probably 
endure  exposure  to  the  weather  as  well  as  the  other. 

2.  That  moisture  reduces  the  strength  of  timber,  whether  that 
moisture  be  the  sap,  or  water  absorbed  after  seasoning.  In  gen- 
eral, seasoned  timber,  or  with  not  more  than  12  per  cent,  mois- 
ture, is  from  75  per  cent,  to  100  per  cent,  stronger  than  green 
timber. 

3.  When  artificially  dried,  timber  contains  a  uniform  percent- 
age of  moisture  throughout,  a  condition  requiring  months  or  even 
years  to  attain  in  air-dried  heavy  timber. 

When  kiln-dried  at  usual  temperatures,  wood  shows  no  loss  of 
strength  compared  with  air-dried  timber  of  the  same  percentage 
of  moisture.  The  effect  of  very  high  temperatures  and  pressures 
(as  used  in  vulcanizing)  is  lower  strengths  than  when  air-dried. 

4.  Large  timbers  are  equal  in  strength  per  square  inch  of  sec- 
tion, tested  every  way,  to  small  timbers,  provided  they  are  equally 
sound  and  contain  the  same  percentage  of  moisture. 

5.  The  tests  seem  to  indicate  that  the  strength  of  woods  of  uni- 
form structure  increases  with  the  specific  gravity  irrespective  of 
species  ;  i.e.,  in  general,  the  heaviest  wood  is  the  strongest.  Oak 
seems  not  to  belong  to  the  list  of  woods  to  which  this  general 
remark  applies. 

The  data  on  properties  of  timbers  must  be  used  with  consider- 
able judgment  and  caution.  Seasoned  wood  will  gain  weight,  to 
the  extent  of  5  to  15  per  cent.,  if  exposed  to  the  weather,  and  this 
excess  will  be  reduced  if  the  wood  is  kept  a  week  in  a  warm  dry 
place. 

Some  of  the  individual  tests  made  by  the  United  States  Forestry 
Division  varied  considerably  from  the  mean  values  given  in  the 
table.  In  the  case  of  tension  tests,  which  varied  most  from  the 
average,  a  few  were  as  low  as  25  per  cent.,  while  others  reached 
190  per  cent,  of  the  mean. 

The  elastic  limit  given  in  connection  with  the  data  from  the 
United  States  Forestry  Division  is  the  relative  elastic  limit  sug- 
gested by  Professor  Johnson,  as  there  is  no  definite  "  elastic 
limit"  in  timber  similar  to  that  in  some   metals.     This  relative 


Physical  Properties  of  Timber  229 

elastic  limit  is  taken  where  the  rate  of  deflection  is  50  per  cent, 
mure  than  it  is  under  initial  loads. 

.Modulus  of  ultimate  bending  is  extreme  fibre  stress  on  beam  at 
rupture.  The  modulus  of  elastic  bending  is  the  fibre  stress  when 
the  rate  of  deflection  is  increased  50  per  cent.  The  modulus  of 
elasticity  is  derived  from  transverse  tests. 


230 


The  Naval   Constructor 


STRENGTH 

Seasoned  timber,  moisture  12  per  cent  and 


Name  of  Material. 


Ash  (American)    .... 

Birch 

Box 

Cedar  (White) 

Cedar  (American  Red)   .     . 

Chestnut 

Cottonwood  (see  Poplar)     . 
Douglas  Spruce  (Oregon  Pine) 

Fir 

Gum 

Hemlock ....... 

Hickory  (American)  average 

Lignum  Vitse 

Mahogany  (Spanish)       .     . 

Maple 

Oregon    Pine  (see  Douglas 

Spruce) 

Oak  (Red) 

Oak  (Black  or  Yellow)   .     . 

Oak  (White) 

Oak  (Live) 

Pine  (Southern  Yellow,  long 

leafed) 

Pine  (Cuban) 

Pine  (Loblolly)      .... 

Pine  (White) 

Poplar 

Spruce  (Northern)      .     .     . 
Spruce  Pine  (Pinus  glabra 

of  So.  States)     .... 
Walnut  (Black)     .... 


o 

©    <»    J 

s  h"i 
-  -  i. 

£  *  53 


17,000 
15,000 
20,000 


10,800 
11,500 


13,000 
13,000 


8,700 
19,600 
11,800 
14,900 
11,150 


10,250 
10,000 
13,600 


13,000 
13,000 
13,000 
10,000 
7,000 
11,000 

12,000 
10,500 


©  © 

a  a 


«  bfi 
A® 

"35  Sm 

<D  O 


+»    00 


©   O) 
S  33 

•pi    +2 

■"    00 

0j 


7,200 
8,000 
10,300 
5,200 
6,000 
5,300 


5,700 

7,100 

5,700 
9,500 
9,900 
8,200 
7,150 


7,200 

7,300 

8,500 

10,400 

8,000 
8,700 
7,400 
5,400 
5,000 
6,000 

7.300 

7,500 


S£ 


g 


'$  on" 

a 

o 
O 


+a  mrr>  © 

pH  >pH  ***      1 

PS  ^ 


1,900 


700 


800 

i,iob 

2,700 


1,800 


2,300 
1,800 
2,200 


1,260 

1,200 

1,150 

700 


1,200 
2,500 


o 

!© 

:  o 
:  a 


ai  bo 


1,100 


400 


500 

1,300 

800 

400 

1,100 


500 


1,100 
1,100 
1,000 


835 
770 
800 
400 


o 

!© 

i  a 


„  ©  o 

CO 


400 

800 


tf 


6,280 
5,600 


1,370 
1,530 


5,890 
2,750 
6,000 


6,350 


4,400 
8,480 

5,600 


2,500 


3,250 
4,700 


Weight  in  Pounds  per 

Cherry 42.0 

Cork 15.6 

Ebony 76.1 


Strength  of  Timber 


231 


OF    TIMBER. 

tinder.    Stresses  given  in  pounds  per  square  inch. 


—  - 

-  .z 

Modulus 

of 
Elasticity. 

•- 

— _  ~ 
0 

Modulus 
of  Blast  lo 

Bending. 

<  IIM'IN  \  K  V    W'oRKlN'  . 

Stke>^. 

23 

41 

Tens. 

Ccllip. 

Tran-. 

7,'. tOO 

•      •      •      • 

1.640,000 
1.045,000 

10.800 

11.700 

7.000 

2,000 
2.000 

2.500 
1.200 
1.400 
1.400 

l.O(X) 

1.000 

1.200 
600 
700 
600 

1.200 
1,200 

1,500 
800 

000 

900 

5.800 

910,000 
1.140,000 

O.300 
7.200 
8,100 

5.800 

*  •      •      • 

•  •      •      • 

6.400 
'  7.800 
11,200 

•      •      • 

1,680,000 
1,530,000 
1,700,000 

2.390,000 

1,255.000 

7.000 

0.400 

1,400 

700 

1,000 

32 

0.500 
7.100 

16,1 

11.700 
9,550 

10,01)0 

7.800 

1,200 

900 

01  M  ) 

750 

l,8oo 
l,5oo 
1,500 

37 
25 

50 
83 
53 

40 

ll,0(il) 

•      ■      •      ■ 

2.0O0 
1.500 
1,500 

1.200 
1,200 

1,200 

9,200 

8.100 
It.  600 
9,040 

10.000 

11,100 

9,200 

6,400 

1.970.000 
1.7  40. 000 
2,090,000 

1,851,500 

•_'."7<>.000 

2,370, > 

2,060,000 
1,390,000 

II.400 
10.800 
13.100 
11,300 

12.600 
13.600 
11,300 

7.000 

6,500 

8,000 

lo. 

8,omi 

9,200 

8.100 

9.000 

1.400 
1.400 
1.700 

900 

000 

1,000 

l,2oo 
1,200 

1.500 

45 
45 
50 

O.500 

lo.oio 

9.4O0 

6.400 

■      •      •      • 

8,400 

1,600 

l.ooo 

1.200 

900 

1.2O0 

1.200 
l,0OO 

1,000 
900 

7. Ml 

600 

Too 

700 
1,000 

1.500 

1,200 

000 

On.) 

900 
900 

33 

24 

26 

30 

38 

8.4HO 
5,7")') 

1.400,000 

1.040.000 
|  1,306,000 

Cubic  Foot  qf  other  Woods, 

Elm 

Mahogany  (Honduras 

35 

) 35 

37 

232 


The  Naval  Constructor 


TABLE    OF   WEIGHT   AND    STRENGTH   OF   WIRE. 


Diameter. 

<  . 

29 

Weight  of 

H 

<   T-   H 

o  rM 

fc  *  S  £M 

M  2  a  >H     . 

3a 

02 

100 
Yards. 

l 
Mile. 

£    ° 
< 

H  H  Kg  H 

In. 

MM. 

Sq.  In. 

Lbs. 

Lbs. 

Yds. 

Lbs. 

7/0 

.500 

12.7 

.1963 

193.4 

3,404 

58  . 

43,975 

6/0 

.464 

11.8 

.1691 

166.5 

2,930 

67 

37,854 

5/0 

.432 

11.0 

.1466 

144.4 

2,541 

78 

32,823 

4/0 

.400 

10.2 

.1257 

123.8 

2,179 

91 

28,144 

3/0 

.372 

9.4 

.1087 

107.1 

1,885 

105 

24,354 

2/0 

.318 

8.8 

.0951 

93.7 

1,649 

120 

21,302 

0 

.324 

8.2 

.0824 

81.2 

1,429 

138 

18,464 

1 

.300 

7.6 

.0707 

69.6 

1,225 

161 

15,831 

2 

.276 

7.0 

.0598 

58.9 

1,037 

190 

13,398 

3 

.252 

6.4 

.0499 

49.1 

864 

228 

11,169 

4 

.232 

5.9 

.0423 

41.6 

732 

269 

9,467 

5 

.212 

5.4 

.0353 

34.8 

612 

322 

7,904 

6 

.192 

4.9 

.0290 

28.5 

502 

393 

6,486 

7 

.176 

4.5 

.0243 

24.0 

422 

467 

5,450 

8 

.160 

4.1 

.0201 

19.8 

348 

566 

4,503 

9 

.144 

3.7 

.0163 

16.0 

282 

700 

3.648 

10 

.128 

3.3 

.0129 

12.7 

223 

882 

2,882 

11 

.116 

3.0 

.0106 

10.4 

183 

1,077 

2,368 

12 

.104 

2.6 

.0085 

8.4 

148 

1,333 

1,903 

13 

.092 

2.3 

.0066 

6.5 

114 

1,723 

1,489 

14 

.080 

2.6 

.0050 

5.0 

88 

2,240 

1,126 

15 

.072 

1.8 

.0041 

4.1 

70 

2,800 

912 

16 

.064 

1.6 

.0032 

3.2 

56 

3,500 

721 

17 

.056 

1.4 

.0025 

2.4 

42 

4,667 

552 

18 

.048 

1.2 

.0018  ' 

1.8 

32 

6,222 

406 

19 

.040 

1.0 

.0013 

1.2 

21 

9,333 

281 

20 

.036 

0.9 

.0010 

1.0 

18 

11,200 

228 

Notes  on  the   Use  of  Wire   Rope       233 


NOTES  ON  THE  USE  OF  WIRE  ROPE. 


- 

- 


-  ■/. 

-  _ 

-  - 

-- 
H 


■_ 
v. 

— 

O 


1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
•21 

23 

24 
25 

'20 

•  > 


< 

28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 


-  ?!  . 

-  r  ■ 
>  -  y. 

3g 


0.63 
1.26 

1.88 
2.51 
3.15 
3.78 
4.42 
5.06 
5.70 
6.34 
6.99 
■  .65 
8.31 
8.97 
9.64 
10.32 
11.00 
11  69 
12.  :■'■'.' 
13.10 
13.82 
14.54 


16.02 
16.78 

17.".''. 
-     • 
19.14 
19  95 
20.78 
21.62 
22.49 
J 
24.28 
25.20 
26.15 
27.12 
2X.12 
29.14 
30.21 


28.63 

19.09 
14.29 

1 1 .42 
9.51 
8.14 
7.11 
6.31 
5.67 
5.14 
4.70 
4.33 
4.01 
3.73 
3.48 
3.27 


3.07 

2.90 

2.74 

2.60 

2.47 

2.35 

2.21 

2.14 

2.05 

1.96 

1.88 

1.80 

1.73 

1.66 

1.60 

1.54 

1.48 

1.42 

1.37 

1.32 

1.28 

1.23 

1.19 


39.08 
78.18 
117.24 
156.26 
195.24 
234.14 
'272.98 
311.74 
350.40 
388.97 
427.41 
465.71 
503.88 
541.90 
579.75 
617.43 
654.90 
692.20 
729.27 
766.12 
802.74 
839.12 
875.23 
911.09 
946.66 
981.94 
1,016.93 
1,051.61 
1.085.97 
1,120.00 
1.153.68 
1,187.02 
1,219.99 
1,252 
1 ,284.81 
1,316.62 
1,348.05 
12379.07 
1.409.67 
1,439.84 


For  Vertical  Winding   at  high  syofU. 
one-tenth  the  breaking  strain  has  in.  i»  adopt,  -a 

as  a  sale  working  Load  ;  it  may,  however,  be 
increased  to  oneeighth,  a rding  to  condi- 
tions of  working.  The  gross  wight  hanging 
over  the  pulley  (including  rope)  being  con- 
sidered the  working  load. 

Hatjijkgon  [ncxihed  Plane.— The  work- 
ins  load  is  usually  taken  at  one-sixth  the 
Slaking  strain,  and  the  following  formula 
for  ascertaining  the  load  has  been  found  from 
experience  to  give  satisfactory  results  : 

Plane,800yds.    Load,20tons. 

Maximum  inclination  7  degs.  or  1  in  8.14. 

Cwts.  Qrs.  Lbs. 

Gravity  of  load,  20  tons  X 

272  98  lbs.  per  ton  = 

Friction  of  load,  20  tons  > 

20  lbs.  per  ton  — 

Gravity  of  rope.  800  yds.  at 

2.15  lbs.,  1720 -f  8.14  = 

Friction  of  rope,  1720-  20  - 
2|  Plough  steel  rope 


49 


=      3 


1 
0 


0 

2 

3 
3 


=    55 


16 

8 

15 
_1 

12 


CtorCOIUNG  WlBE  ROPE.—- A  reel  or  turn- 
table should  be  used  to  avoid  "kinks  or 
sharp  bends. 

LUBRICATION  OF  ROPES.— Both  winding 
and  hauling  ropes  Bhould  be  well  oiled  topro- 
U7ne  duration.  The  winding  ''ope  rspeeialh 
ought  to  have  frequent  appucations  of  heavy- 
bodied  hydrocarbon  oil,  which  should  be 
well  rubbed  into  the  interstices  with  a  swaD, 
a,  itis  important  that  the  inside  of  the  rope 
should  benefit  as  well  as  the  outside  by  its 
application. 

X  B  —  An  unlubricated  rope  stood  16,000 
bends  before  fracture,  whilst  the  same  rope 
lubricated  stood  38,700. 


I 


234 


The   Naval   Constructor 


PROOF  OR  TEST  LOAD  FOR  CHAINS. 

d  ■=.  Diameter  of  Iron  in  Inches. 

The  Admiralty  Rules  are  : 

Test  Load  in  Tons  =  18r72  for  Studded  Links. 
Test  Load  in  Tons  =  12d-  for  Unstudded  Links. 


d. 

18  d\ 

12  d2. 

d. 

18  d2. 

12  d2. 

d. 

18  d2. 

12  d2. 

i 

.75 

3 

3 

10.1 

6.7 

n 

40.5 

27.0 

6 

T5 

■     •     • 

1.17 

13 

IB 

11.9 

7.9 

ii 

47.5 

31.7 

1 

•     •      • 

1.69 

7 

s 

13.8 

9.2 

n 

55.1 

36.7 

I7B 

3.45 

2.30 

I5 
IB 

15.8 

10.5 

17 

x8 

63.3 

42.2 

1 
2 

4.50 

3.00 

1 

18.0 

12.0 

2 

72.0 

4S.0 

9 
IS 

5.70 

3.80 

1| 

22.8 

15.2 

01 

81.3 

54.2 

e 
B 

7.03 

4.69 

1J 

28.1 

18.7 

2£ 

91.1 

60.7 

n 
IS 

8.51 

5.67 

1| 

34.0 

22.7 

D3 

101.5 

67  7 

The  practice  at  Elswick  is  to  make  the  test  load  10  per  cent, 
higher  than  the  Admiralty  test  load. 


STRENGTH  OF  CHAIN  CABLES  (AMERICAN). 


£ 

Break- 

H S3 

ing 

Stress 

Recommended 

Admiralty 

Probable  Aver- 
age   XjLT'TArArrTi' 

of  Iron 

Proof  Load  on 

Proof  Load  on 

St KENT 

,TH     (IK 

in  Lbs. 

PER  SQ. 

In. 

Cable. 

Cable. 

Cable. 

In. 

Lbs. 

Tons. 

Lbs. 

Tons. 

Lbs. 

Tons. 

1 

55,596 

33,840 

15.11 

40,320 

18.00 

71,172 

31.77 

1A 

55,073 

37,820 

16.88 

45,517 

20.32 

79,544 

35.51 

U 

54,589 

42,053 

18.77 

51,030 

22.78 

88,445 

39.48 

iT% 

54,138 

46,468 

20.74 

56,857 

25.38 

97,731 

43.63 

n 

53,715 

51,084 

22.81 

63,000 

28.12 

107,440 

47.96 

lfss 

53,317 

55,903 

24.96 

69,457 

31.01 

117,577 

52.49 

H 

52,941 

60,920 

27.20 

76,230 

34.03 

128,129 

57.20 

1IB 

52,584 

66,138 

29.53 

83,317 

37.20 

139,103 

62.10 

U 

52,245 

71,550 

31.94 

90,720 

40.50 

150,485 

67.18 

1    9 

*IB 

51,922 

77,159 

34.45 

98,437 

43.95 

162,283 

72.45 

H 

51,613 

82,956 

37.03 

106,470 

47.53 

174,475 

77.89 

1  16 

51,317 

88,947 

39.71 

114,817 

51.26 

187,075 

83.52 

If 

51,033 

95,128 

42.47 

123,480 

55.12 

200,074 

89.32 

1« 

50,760 

101,499 

45.31 

132,457 

59.13 

213.475 

95.30 

1| 

50,498 

108,058 

48.24 

141,750 

63.28 

227,271 

101.46 

115 

1lS 

50,245 

114,806 

51.25 

151,357 

67.57 

241,463 

107.80 

2 

50,000 

121,737 

54.35 

161,280 

72.00 

256,040 

114.30 

Strength  of  Small   Chains 


235 


STRENGTH  OF  SMALL  CHAINS. 
THE  FOLLOWING  RULES  ARE  BASED  ON  EXPERIMENTS  CAR- 
RIED OUT  BY   PROF.    H.S.    HALE  SHAW  ON   SMALL  CHAINS. 
LESS  THANHS 


SINGLE  JACK 
W  =  7850d2 


Fig.  102. 


Fig.  103. 


m 


b 


_ZT 


DOUBLE  JACK 
)    W  =  1B,700ds 


ORDINARY  WELDED 
W=39,250d2 


Fig.  104. 


TRIUMPH"  WELCLESS 
^MACHINE  MADE 
W78,500d* 


w  =  breaking  load  in  lbs.    d  =  si2e  of  chain  in  inches. 

the  6ar£  load  may  be  taken  as  one  quarter  of  breaking  load. 

Fig.  105. 


236 


The  Naval  Constructor 


DIMENSIONS    AND  WEIGHT    OF  CHAIN  CABLES  * 


Size  of  Links  (Out- 

NUMBER 

Weight  per  Fathom. 

Diameter 

side). 

of  Links 

in  One 

Fathom. 

of  Iron. 

Length. 

Width. 

Studded 
Links. 

Open 
Links. 

In. 

In. 

In. 

Lhs. 

Lbs. 

1 

°1B 

Q  9 
•'IB 

191 

57.8 

52.9 

h\ 

6$ 

Ql  1 

18* 

64.7 

60.1 

H 

6i 

4 

18 

77.7 

69.7 

1$ 

6| 

*  8 

17 

84.8 

77.4 

11 

7 

*& 

16 

94.9 

86.8 

1A 

7  B 
'lB 

Vb 

15£ 

102.9 

95.2 

if 

7  9„ 
'tb 

4|| 

15 

115.5 

106.2 

l& 

8 

5A 

14 

121.7 

113.0 

u 

8i 

°1B 

13i 

134.3 

124.2 

ll95 

»1b 

f;  9 
"IB 

13 

144.6 

134.9 

If 

9 

5^ 

12* 

160.0 

146.7 

m 

91 

6 

12 

170.1 

157.3 

if 

9| 

6& 

HI 

183.2 

168.9 

m 

10i35 

6i75 

11 

192.9 

179.1 

il 

10i5B 

61 

11 

215.6 

199.1 

1  16 
■■^lB 

10 1 

6| 

lOJ 

225.0 

209.2 

2 

103 

7i 

10 

240.8 

219.9 

2  A 

Ht6s 

7§ 

10 

261.4 

240.5 

n 

int. 

7| 

91 

272.1 

250.7 

2i3s 

12 1 

7| 

9 

279.1 

258.8 

ULTIMATE    OR   BREAKING   STRENGTH 

OF    CHAINS. 

The  breaking  stress  of  the  iron  of  which  chains  are  made  varies 
with  the  diameter  of  the  bar,  being  less  the  greater  the  diameter. 

If  /=  breaking  stress  of  iron  in  tons  per  square  inch, 

and  d  =  diameter  of  bar  in  inches, 

then  /=  26.2  -  2.4  d. 

Breaking  load  of  chain  in  tons  =  W=  1.22  d2  (26.2  —  2.4  d). 

This  formula  allows  for  the  bending  action,  and  for  the  loss  of 
strength  due  to  the  weld. 

The  following  table  gives  values  of  W  for  various  values  of  d, 
calculated  by  the  above  formula  : 


d 

w. 

d. 

w. 

d. 

w. 

d. 

W. 

I 

1.95 

I 

11.8 

1 

29.0 

If 

82.2 

5 

IB 

3.03 

1 1 

IB 

14.2 

If 

36.3 

11 

93.1 

3 

4.34 

1 

16.7 

if 

44.2 

2 

104.4 

7 

5.87 

]  3 
IB 

19.5 

If 

52.8 

2£ 

116.2 

7.62 

i 

22.5 

n 

62.0 

2i 

128.5 

I9B 

9.59 

11 

25.7 

if 

71.8 

2§ 

141.1 

*  From  Report  of  Committee  of  Government  Board,  IT.  S.  A.,  1879. 


Elements  of  Angles 


237 


CHAPTER   III. 


ELEMENTS    OF   ANGLES. 


Size  in* 

THIi  k- 

Area 

Weight 

Moments  of  Inertia. 

I>«  HI  -. 

NKSS. 

ix  Square 

per  Foot  eh 

I  N  <  1 1  F  - . 

Pounds. 

Axis,  AB. 

Axis,  /V. 

8      X8 

1 

7.7."> 

26.4 

48.47 

19.60 

8J  X  8J 

1 

15.29 

52.8 

94.14 

39.01 

6      x  6 

3 

4.36 

14.8 

15.37 

6.20 

61   X  61 

¥ 

10.65 

35.9 

36.09 

15.48 

5      X  5 

3.61 

12.3 

8.73 

3.54 

51   X  51 

is 
IS 

5.77 

29.4 

20.72 

9.09 

4      X  4 

t 

2.40 

8.2 

3.69 

1.50 

*l    X41 

5.69 

18.6 

-.71 

::.v_> 

X  3£ 

i6s 

2.09 

7.1 

2.45 

(1.99 

3f   X3| 

1 

4.06 

13.7 

4.60 

1.97 

3      X  3 

1 

1.44 

4.9 

1.25 

0.50 

•-'  1X21 

i 

3.51 

ll.r, 

3.01 

1 .32 

$ 

1.31 

4.5 

0.95 

0.39 

3      X  3 

* 

2.70 

8.6 

2.11 

0.90 

21   X  2* 

3 

I 

0.1K) 

3.1 

0.54 

0.22 

-  .     •    -'  . 

2.33 

7.8 

1.33 

0.59 

2  J    •    - 

a 

0.81 

•_'.7 

0.39 

0.16 

.>  -    .    ..  - 

-15   *•    - 

1.66 

5.4 

0.85 

0.37 

2      X  2 

h 

0.71 

2.5 

0.27 

0.11 

2,38  X  2  A 
1?    X  1} 

i 

1.47 

4.8 

0.61 

0.26 

"38 

0.62 

2.1 

0.18 

0.08 

\\%  i  » 

1.28 

4.1 

0.39 

0.18 

I 

0.36 

1.2 

0.08 

0.03 

H  x  l  J 

1 

1.14 

3.5 

0.29 

0.13 

•  li 

I 

0.30 

1.0 

0.06 

0.02 

if  x  if 

| 

0.62 

2.0 

0.10 

0.04 

1       X  1 

J 

0.23 

0.8 

0.02 

0.01 

1  i  >  H 

• 

0.49 

1.5 

0.05 

0.02 

238 


The  Naval   Constructor 


ELEMENTS    OF   ANGLES. 


Fig.  106. 


Distance  from 

Radii  or  Gyrat  on. 

Resistance. 

Base  to 

Neutral  Axis. 

Axis  AB. 

Axis  EF. 

Axis  AB. 

d. 

2.50 

1.59 

8.34 

2.19 

2.48 

1.60 

16.18 

2  43 

1.88 

1.19 

3.53 

1.64 

1.86 

1.21 

8.43 

1.19 

1.56 

0.99 

2.42 

1.39 

1.54 

1.02 

5.76 

1.65 

1.24 

0.79 

1.28 

1.12 

1.24 

0.82 

3.10 

1.34 

1.08 

0.69 

0.98 

0.99 

1.06 

0.70 

1.84 

1.13 

0.93 

0.59 

0.58 

0.84 

0.93 

0.61 

1.39 

1.02 

0.85 

0.55 

0.48 

0.78 

0.88 

0.58 

1.02 

0.93 

0.77 

0.49 

0.80 

0.70 

0.76 

0.50 

0.75 

0.84 

0.69 

0.44    ' 

0.24 

0.63 

0.72 

0.47 

0.50 

0.75 

0.62 

0.39 

0.19 

0.58 

0.64 

0.42 

0.40 

0.68 

0.54 

0.36 

0.15 

0.51 

0.55 

0.38 

0.30 

0.63 

0.47 

0.28 

0.07 

0.42 

0.50 

0.34 

0.25 

0.57 

0.41 

0.26 

0.06 

0.35 

0.40 

0.25 

0.11 

0.43 

0.29 

0.21 

0.03 

0.30 

0.32 

0.20 

0.07 

0.37 

Elements  of  Bulb  Angles 


239 


ELEMENTS    OF   BULB    ANGLES. 


to 
s:  "- 

10 

~~  —  "■ 

M          ^^       " 

z  - 

■— 1 

• 

s  --  g 

3  =  ~ 

?  -- 

- 

MOMKNTS   OF 

Lnebtj  \. 

Sqi  aki:  of 

Radius 

of  Gyration. 

Radius 
of 

Gyration. 

Axis 
AB. 

Axis 
(  D. 

Axis 
EF. 

Axis 
AB. 

Axis 
CD. 

Axis 
EF. 

0.68 

Axis 

.  /  /;. 

3.50 

A  sis 
CD. 

0.96 

Axis 
EF. 

7.70 

26.2 

94.17 

7.11 

5.22 

12.23 

0.92 

0.82 

10 

11.24 

38.2 

136.41 

11.93  9.19 

12.14 

1.06 

0.82 

3.48 

1.03 

0.90 

0 

6.74 

229 

67.67 

6.58  4.68 

10  04 

0.98 

0.69 

3.17 

0.99 

0.83 

9 

9.56 

32.5 

95.71 

10.61 

7.60 

10.01 

1.11 

0.79 

3.16 

1.05 

0.89 

8 

5.62 

19.1 

44.69 

4.09 

3.06 

7.95 

0.73 

0.54 

2.82 

0.85 

0.74 

8 

7.77 

26.4 

61.63 

6.43 

4.83 

7.93 

0.83 

0.62 

2.82 

0.91 

0.79 

i 

479 

16.3 

29.74 

3.73 

2.66 

6.21 

0.78 

0.56 

2.49 

0.88 

0.75 

i 

6  11 

21.8 

39.67 

5.58 

3.93 

6.19 

0.87 

0.61 

2.49 

0.93 

0.7N 

6 

3.91 

13  3 

18.31 

3.24 

2.26 

4.68   083 

0.58 

2.16 

0.91 

0.76 

6 

5.24 

17.8 

24 

4.81 

:;  29 

465  0.92 

0.63 

2.16 

0.96 

0  79 

•  i 

2  '.'7 

10.1 

9.84 

1.76 

1.52 

3.31 

0.59 

0.51 

1.82 

0.77 

0.72 

5 

3.97 

13.5 

13.07 

2.64 

1.86 

3  29 

0.66 

0.47 

1.81 

0.82 

0.68 

240 


The  Naval  Constructor 


ELEMENTS    OF   DECK   BEAMS. 


Fig.  108 


fc  OS 

p-c  y 

a  ^  se 

H 

K  g    • 
C  c  * 

Moments  of 
Inertia. 

Square  of 
Radius  of 
Gyration. 

Radius  of 
Gyration. 

111 

Ph 

Axis 
AB. 

Axis 
CD. 

Axis 
AB. 

Axis 
CD. 

Axis 
AB. 

Axis 
CD. 

9.51 

32.2 

179.33 

6.36 

18.86 

0.67 

4.34 

0.82 

Hi 

13.41 

45.6 

224.19 

8.14 

16.72 

0.61 

4.09 

0.78 

10 

8.20 

28.0 

118.55 

6.08 

14.46 

0.74 

3.80 

0.86 

10 

11.32 

38.6 

145.77 

7.54 

12.88 

0.67 

3.59 

0.82 

9 

7.35 

25.0 

84.99 

4.85 

11.56 

0.66 

3.40 

0.81 

9 

9.60 

32.6 

100.68 

5.78 

10.49 

0.60 

3.24 

0.77 

8 

6.17 

21.0 

57.75 

3.58 

9.36 

0.58 

3.06 

0.76 

8 

8.43 

28.6 

70.19 

4.44 

8.33 

0.53 

2.89 

0.73 

t 

5.32 

18.0 

36.99 

2.56 

6.95 

0.48 

2.64 

0.69 

7 

7.29 

24.5 

45.32 

3.26 

6.22 

0.45 

2.49 

0.67 

6 

4.27 

14.5 

21.83 

1.62 

5.11 

0.38 

2.26 

0.62 

6 

5.77 

19.6 

26.50 

2.07 

4.59 

0.36 

2.14 

0.60 

5 

3.39 

11.5 

11.96 

1.01 

3.53 

0.30 

1.88 

0.55 

5 

4.64 

15.8 

14.64 

1.29 

3.16 

0.28 

1.78 

0.53 

Elements  of   Deck   Beams 


241 


ELEMENTS    OF   DECK   BEAMS.—  (Continued.) 


00 

H 

= 

t—i 

>-c 

H 

s: 

— 

Resistance,  Axis  Ali. 

■a  •- 

-  /   _' 

'  c  c 

<  z  - 

-  _  L. 

■  —  H 

—  _ 
_  - 

■r  ^  § 

<  z 

< 

0 

H         IB 

B  -  - 
r  <H 
gCD 

h  H  g 

a  H 

w   H 

-<? 

C  -j  "^ 

^  -  c 

c  -"*" 

i  r  _: 

_  z  < 

<2Z 

Coefficient  for 
Deflection. 

Max i mi  m  Load  in 
Net  Tons. 

Distance  d  from 

Base  to 

Neutral  Axis. 

Distributed 
Load. 

Centre 
Load. 

114 

27.9 

0.60 

148.7 

3.22 

.0000089 

.0000143 

48.6 

5.07 

in 

36.0 

0.60 

191.9 

3.22 

.0000071 

.0000114 

119.4 

5.27 

10 

20.7 

0.54 

110.5 

2.86 

.0000135 

.0000217 

40.8 

4.28 

10 

26.4 

0.54 

140.8 

2.86 

.0000107 

.0000172 

96.4 

4.48 

9 

1G.7 

0.48 

88.9 

2.55 

.0000188 

.0000303 

39.0 

3.90 

9 

20.3 

0.48 

108.3 

2.55 

.0000159 

.0000256 

79.0 

4.04 

8 

12.8 

0.43 

68.1 

2.28 

.0000277 

.0000446 

32.4 

3.48 

8 

16.0 

0.43 

85.5 

2.28 

.0000228 

.0000367 

72.2 

3.62 

7 

9.3 

0.38 

49.8 

2.02 

.0000432 

.0000695 

30.2 

3.04 

7 

11.8 

0.38 

62.9 

2.02 

.0000352 

.0000568 

64.6 

3.16 

G 

6.4 

0.32 

34.3 

1.69 

.00007:33 

.0001180 

24.0 

2.61 

6 

8.1 

0.32 

43.0 

1.69 

.0000604 

.0000972 

50.2 

2.71 

5 

4.3 

0.26 

22.9 

1.39 

.0001337 

.0002147 

21.4 

2.22 

5 

6.4 

0.26 

28.9 

1.39 

.0001093 

.0001755 

42.8 

2.30 

242 


The   Naval   Constructor 


ELEMENTS    OF   TEES.  — Uneven  Legs. 


Size 

M    S    * 

P3  k 

M    A     3Q 

^    KH    •**, 
A,           H 

Moments  of 
Inertia. 

Resistance. 

Radius  of 
Gyration. 

"  <  V. 

in 
Inches. 

■<  <  a 

H  &  3 

^•°s 

HOC 

^  «  c 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

<j  32— i 

^Ph 

AB. 

CD. 
13.81 

AB. 

CD. 

AB. 

CD. 

6   x4i 

8.21 

28.2 

14.74 

4.71 

4.60 

1.33 

1.29 

1.37 

6X4 

4.61 

15.6 

5.82 

8.19 

1.92 

2.73 

1.12 

1.33 

0.97 

6    X5J 

11.58 

39.0 

28.68 

18.75 

8.19 

6.25 

1.57 

1.27 

1.75 

5    X3i 

4.95 

17.0 

5.29 

5.47 

2.17 

2.19 

1.03 

1.05 

1.06 

5    X4 

4.54 

15.3 

6.16 

5.41 

2.11 

2.16 

1.17 

1.09 

1.08 

4X2 

1.93 

6.5 

0.53 

1.75 

0  34 

0.87 

0.52 

0.95 

0.46 

4    X3 

2.67 

9.0 

1.99 

2.10 

0.90 

1.05 

0.87 

0.89 

0.78 

4    X3 

3.05 

10.2 

2.24 

2.44 

1.02 

1.22 

0.85 

0.89 

0.81 

4    X4| 

4.29 

14.6 

7.87 

2.80 

2.50 

1.40 

1.37 

0.81 

1.37 

4|x3£ 

4.65 

15.8 

4.93 

3.67 

2.05 

1.63 

1.03 

0.89 

1.11 

4    X4| 

3.38 

11.4 

6.31 

2.11 

1.96 

1.06 

1.37 

0.79 

1.28 

3£  X  3 

2.11 

7.0 

1.65 

1.18 

0.75 

0.67 

0.88 

0.75 

0.80 

3|X3 

2.46 

8.5 

1.91 

1.41 

0.88 

0.81 

0.88 

0.75 

0.83 

3    X  1J 

1.20 

4.0 

0.18 

0.60 

0.16 

0.40 

0.39 

0.71 

0.36 

3    X2i 

1.46 

50 

0.78 

0.60 

0.42 

0.40 

0.73 

0.64 

0.66 

3    X2£ 

1.76 

6.0 

0.93 

0.74 

0.51 

0.49 

0.73 

0.65 

0.68 

3    X2i 

2.06 

7.0 

1.08 

0.89 

0.60 

0.59 

0.72 

0.66 

0.71 

3    X2| 

2.38 

8.0 

1.32 

0.91 

0.78 

0.61 

0.74 

0.62 

O.SO 

3    X  3£ 

2.46 

8.3 

2.82 

0.89 

1.17 

0.59 

1.07 

0.60 

1.08 

3    X3£ 

2.81 

9.5 

3.19 

1.04 

1.33 

0.69 

1.07 

0.61 

1.10 

2f  X  1| 

1.96 

6.6 

0.56 

0.60 

0.50 

0.44 

0.54 

0.56 

0.64 

2|X2 

2.14 

7.2 

0.82 

0.61 

0.G6 

0.44 

0.62 

0.54 

0.75 

2*X  H 

0.97 

3.3 

0.10 

0.33 

0  11 

0.26 

0.32 

0.58 

0.31 

2£  X  2J 

1.68 

5.7 

1.16 

0.43 

0.60 

0.34 

0.83 

0.51 

0.83 

2^X3 

1.76 

6.0 

1.48 

0.44 

0.71 

0.35 

0.92 

0.50 

0.93 

2iX    ft 

0.66 

2  2 

0.01 

0.24 

0.03 

021 

0.14 

0.60 

0.17 

2    X    ft 

0.60 

2^0 

0.01 

0.17 

0.03 

0.17 

0.14 

0.53 

0.17 

2    X  1£ 

0.62 

2.0 

0.04 

0.16 

0.05 

0  16 

0.24 

0.51 

0.23 

2    X  1 

0.72 

2.5 

0.05 

0.17 

0.07 

0.17 

0.26 

0.49 

0.27 

2X1* 

0.91 

3.0 

0.16 

0.17 

0.15 

0.17 

0.42 

0.44 

0.45 

1|  X  1ft 

0.56 

1.9 

0.05 

0.11 

0.06 

0.13 

0.30 

0.45 

0.24 

ilxU 

1.04 

3.5 

0.12 

0.21 

0.14 

0.24 

0.35 

0.45 

0.40 

i|x  it 

0.41 

1.4 

0.02 

0.07 

0.03 

0.09 

0.22 

0.41 

0.21 

iix  il 

0.35 

1.2 

20.0 

0.03 

0.03 

0.05 

0.24 

0.30 

0.22 

Elements  of  Tee   Bars 


243 


ELEMENTS   OF   TEES.  —  Even  Legs. 


■_• 

Moments 

Radius  of 

-  <  ■ 

—    —    '*■ 

ok  Inertia. 

Resis 

r.vxc  E. 

Gyration. 

a  B  CO 

Size  in 
In<  HB8. 

'_"    r    % 

2  —  - 

A  <  X 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

— 

AB. 

CD. 

AB. 

CD. 

AB. 

CD. 

4    X4 

3.10 

10.9 

4.70 

2.20 

1.64 

1.10 

1.23 

0  85 

1.15 

4X4 

3.98 

13.7 

;».7i) 

2.79 

2.02 

1.40 

1.20 

0.84 

1.18 

oh  X  oh 

2.08 

7.0 

2.27 

1.03 

O.V.I 

0.59 

1.04 

0.71 

0.94 

3£  X  34 

2.65 

9.0 

2.83 

1.32 

1.16 

0.75 

1.03 

0.71 

1.06 

^x^ 

3.24 

11  0 

:;.»;i 

1.75 

1 .4!) 

1.00 

105 

0.73 

1.07 

3X3 

1.91 

6.5 

1.57 

0.75 

0.74 

0.50 

0.91 

0.62 

0.87 

3X3 

2.27 

1  .  1 

1.82 

0.89 

osr, 

0.60 

o.v.i 

0.62 

0.88 

2*X2£ 

1.47 

5.0 

0.79 

0..-..S 

0.44 

0.30 

0.73 

0.51 

0.69 

2k  X  2J 

1.71 

5.8 

0.95 

0.48 

0.55 

0.38 

0.75 

0.53 

0.76 

2\  X  2i 

2J  X  2J 

1.94 

6.6 

l.ns 

0.56 

0.63 

0.45 

0.75 

0.54 

0.79 

1.18 

4.0 

0.51 

0.27 

0.31 

0.24 

0.66 

0.48 

0.62 

2|  x  2i 

1.18 

4.0 

0.52 

0.26 

0.33 

0.23 

0.66 

0.47 

0.65 

2X2 

1.03 

3.5 

0.37 

0.18 

0.26 

0.18 

0.60 

0.41 

0  60 

If  X  1J 

0.71 

2.4 

0.19 

0.09 

0.15 

0.10 

0.52 

0.36 

0.51 

H  X  H 

0.59 

2.0 

0.12 

0.06 

0.12 

0.08 

0  45 

0.32 

0.47 

lix  lj 

0.44 

i.r» 

0.07 

0.04 

0.09 

0.06 

0.40 

0.30 

0.43 

1    X  1 

0.29 

1.0 

0.03 

o.o-j 

0.05 

0.04 

0.32 

0.26 

0.38 

244 


The   Navai   Constructor 


ELEMENTS    OF   Z   BARS. 


H 

H 

Moment 

OF 

£  H  t» 

Inertia 

Resistance 

"!  2  W 

W  O  0 

Sizes  in  Inches. 

h  to  g 

Mfc 

Axis 

Axis 

Axis 

Axis 

Axis 

AB. 

CD. 

EF. 

0.59 

AB. 

CD. 

2  f   x  3      X  2f  X   J 

1.94 

6.60 

2.81 

2.61 

1.9 

1.0 

■^T6  X  3xg  X  2fs  X  i5g 

2.44 

8.29 

3.52 

3.38 

0.74 

2.3 

1.3 

n  X  3JX  2}  X  f 

2.94 

10.00 

4.34 

4.22 

0.92 

2.8 

1.7 

98  1   y   q         v   921    v     7 
*>\i2  X  o        X   -^32  X   jg 

3.25 

11.15 

4.20 

4.24 

0.95 

2.8 

1.7 

on   y  qi    v-  91 1  v   is 
"iu   X   Oa2  A   ^ig  X    55 

3.51 

11.93 

4.54 

4.64 

1.01 

3.0 

1.9 

923    v    Q   1      y    923    y      1 
^3  2    X    «>I3    X    ^32    X     2 

3.75 

12.75 

4.88 

5.04 

1.11 

3.2 

2.0 

2$  X4      X2i  X  J 

2.32 

7.88 

5.95 

3.47 

0.95 

3.0 

1.3 

915    y    11      y    015    y      6 
^15  X  *ig  X   ^jg  X   jg 

2.91 

9.89 

7.52 

4.49 

1.23 

3.7 

1.6 

3      X  4  i  X  3      X| 

3.52 

11.90 

9.14 

5.58 

1.53 

4.4 

2.0 

m  X  4      X  2H  X  & 

3.96 

13.46 

9.40 

6.09 

1.63 

4.7 

2.2 

3j2  X  4T15  X  335  X   5 

4.56 

15.50 

10.92 

7.21 

1.94 

5.4 

2.6 

335  X  4  8    x  3g2  X  ig 

5.16 

17.54 

12.40 

8.40 

2.27 

6.0 

3.0 

3^6  X  4      x3i'BXf 

5.55 

18.80 

12.11 

8.73 

2.32 

6.1 

3.2 

3*  X4|   X3i  xi* 

6.14 

20.87 

13.52 

9.95 

2.67 

6.7 

3.6 

3TJ  X  4i   X  3/g  X   | 

6.75 

22.95 

14.97 

11.24 

3.03 

7.3 

4.0 

3j%  X  5      X  3-j3g  X  ig 

3.36 

11.42 

13.14 

5.81 

1.86 

5.3 

1.9 

3|   X5^X3|   X   § 

4.05 

13.77 

15.93 

7.20 

2.28 

6.3 

2.4 

3Tg  X  5  g   X  3TS  X  is 

4.75 

16.15 

18.76 

8.67 

2.75 

7.3 

2.8 

355  X  5      X  3375  X  ? 

5.23 

17.78 

19.03 

8.77 

2.76 

7.6 

3.0 

335  X  5Tg  X  33?2  X  ig 

5.91 

20.09 

21.65 

10.19 

3.20 

8.6 

3.4 

3g2  X  5  8    X  052  X   f 

6.60 

22.44 

24.33 

11.70 

3.73 

9.5 

3.9 

3|   X5i   X  3 i  X  tt 

6.96 

23.66 

23.68 

11.37 

3.59 

9.5 

3.9 

3Tg  X  ^xs  X  3j5g  X   ~i 

7.64 

25.97 

26.16 

12.83 

4.12 

10.3 

4.4 

3|X6j   X3|X| 

4.59 

15.61 

25.32 

9.11 

3.11 

8.4 

2.8 

3Tg  X  615  X  3Tg  X  ig 

5.39 

18.32 

29.80 

10.95 

3.74 

9.8 

3.3 

3f  X  6i  X3f  x   h 

6.19 

21.05 

34.36 

12.87 

4.37 

11.2 

3.8 

3|  X  6      X  3|  X  T9S 

6.68 

22.71 

34.64 

12.59 

4.37 

11.6 

3.9 

3js  X  6TS  X  3jg  X   % 

7.46 

25.36 

38.86 

14.42 

4.92 

12.8 

4.4 

3f  X6|X3|  X  U 

8.25 

28.05 

43.18 

16-34 

5.66 

14.1 

5.0 

3|  X  6      X3|  X  J 

8.64 

29.37 

42.12 

15.44 

5.61 

14.0 

4.9 

3yg   X    Dig   X   3yg  X    IS 

9.38 

31.89 

46.13 

17.27 

6.16 

15.2 

5.5 

3Sx6ix3Sxi 

10.16 

34.54 

50.22 

19.18 

6.85 

16.4 

6.0 

Klements   of  Z    Bars 


2  i  5 


ELEMENTS    OF    Z    BARS. 


Fig. 

110. 

Coefficient  eh 

Coeffk  ient  for 

q  . 
<  5 

i;  \  LIT  OF 

Gykation 

Xf.t    Tons    fob 
Greatest  Safe 
LoadDistaxce. 

Deflf.i  xiok 
about  axis  ab. 

:  g 

5  - 
Z  H 
1/. 

Axis 
AB. 

Axis 
CD. 

Least 
Axis 
EF. 

Fibre 

Stress 

16,000 

Lbs. 

Fibre 

Str.-- 
12,000 
Lbs. 

7.5 

Distribu- 
ted. 

Centre. 

1.20 

1.16 

0.55 

10.0 

.0005694 

.0009167 

11.0 

1.20 

1.18 

0.55 

12.3 

9.2 

.0004545 

.0007317 

14.4 

1.21 

1.20 

0.56 

14.8 

11.1 

.0003687 

.0005937 

18.0 

1.13 

1.14 

0.54 

14.9 

11.2 

.0003809 

.0006132 

20.4 

1.14 

1.15 

0.54 

16.0 

12.0 

.0003524 

.0005674 

22.2 

1.14 

1.16 

0.55 

17.0 

12.8 

.0003279 

.0005279 

24.li 

l.eo 

1.22 

0.64 

15.9 

11.9 

.0002689 

.0004329 

13.6 

1.61 

1.24 

0.65 

19.7 

14.8 

.0002128 

.0003426 

18.2 

1  62 

1.26 

0.66 

23.6 

17.7 

.0001750 

.0002817 

23.0 

154 

1 .24 

0.64 

25.1 

18.8 

.0001702 

.0002740 

26.6 

1 .:.-. 

1.27 

0.65 

23.7 

21.5 

.0001465 

.0002359 

31.2 

1  .."•"> 

1.28 

0.66 

32.1 

24.1 

.0001290 

.0002077 

35.8 

1.48 

1.26 

ii.!;.-, 

32.3 

24.2 

.0001321 

.0002127 

39.0 

1.48 

1.27 

(i..;(; 

35.5 

26.6 

.00011X3 

.0001905 

43.6 

1.49 

l.i".  t 

0.67 

38.7 

29.0 

.0001069 

.0001721 

48.6 

1.98 

1.32 

0.74 

28.0 

21.0 

.0001218 

.0001961 

21.4 

1.98 

1.33 

0.75 

33.6 

25.2 

.0001005 

.0001618 

27.0 

1 .99 

1.35 

0.76 

39.1 

29.3 

.0000853 

.0001373 

32.8 

1.91 

1.30 

0.73 

40.6 

30.5 

.0000841 

.0001: 554 

37. 6 

1.91 

1.31 

H.71 

45.6 

34.2 

.0000739 

.0001190 

43.2 

1.92 

1.33 

n.7.-, 

50.6 

:;.s.(i 

.0000658 

.0001059 

4:  mi 

1.84 

1.28 

0.72 

50.5 

37.9 

.0000676 

.0001088 

53.2 

i.>r. 

1.30 

u.7;'. 

55.1 

41.3 

.0000612 

.IHXI0984 

59.0 

■_■  36 

1.41 

0.82 

45.0 

33.8 

.0000632 

.0001017 

30.8 

2.35 

1.4;; 

ii  -;; 

52.4 

39.3 

.0000537 

.0000864 

37.6 

2.36 

1.44 

0.84 

• 

44.9 

.0000466 

0000750 

44.  i; 

2.28 

l.:;: 

0.81 

61.6 

46.2 

.00004  62 

.0000744 

50.2 

1.:::' 

0.81 

68  1 

51.3 

.0000412 

.0000663 

57.0 

2.29 

1.41 

ii.  v; 

75.2 

56.4 

.OOOii.;:  i 

.0000596 

64.0 

2.21 

1.34 

0.81 

74.9 

56.2 

.0000380 

.0000612 

69.0 

2.22 

1.36 

0.81 

81.2 

00.9 

.0000347 

.ikk  10559 

76.0 

■  )  •>.  i 

1.37 

0.82 

87.5 

65.6 

.0000319 

.OOi' 

246 


The   Naval   Constructor 


BENDING   MOMENTS    OF  PINS. 


Moment  =  —  I)zf. 


Diameter 


_•  (?) 


IT 

32 


DlAM- 

Area  of 

Moments  in  Inch-Pounds  for 
Strains  of 

Fibre 

E  PER    OF 

Pin  in 
Inches. 

Pin  in 

Square 

Inches. 

15,000  Lbs. 

per 
Sq.  Inch. 

20,000  Lbs. 

per 
Sq.  Inch. 

22,000  Lbs. 

per 
Sq. Inch. 

25,000  Lbs. 

per 
Sq.  Inch. 

2,450 

1 

0.785 

1,470 

1,960 

2,160 

H 

0.994 

2,100 

2,800 

3,080 

3,500 

if 

1.227 

2,880 

3,830 

4,220 

4,790 

if 

1.485 

3,830 

5,100 

5,620 

6,380 

H 

1.767 

4,970 

6,630 

7,290 

8,280 

If 

2.074 

6,320 

8,430 

9,270 

10,500 

If 

2.405 

7,890 

10,500 

11,570 

13,200 

If 

2.761 

9,710 

12,900 

14,240 

16,200 

2 

3,142 

11,800 

15,700 

17,280 

19,600 

2J 

3.547 

14,100 

18,800 

20,730 

23,600 

21 

3.976 

16,800 

22,400 

24,600 

28,000 

2f 

4.430 

19,700 

26,300 

28,900 

32,900 

2* 

4.909 

23,000 

30,700 

33,700 

38.400 

2f 

5.412 

26,600 

35,500 

39,000 

44,400 

2! 

5.940 

30,600 

40,800 

44,900 

51,000 

23 

6.492 

35,000 

46,700 

51,300 

58,300 

3 

7.069 

39,800 

53,000 

58,300 

66,300 

21 

7.670 

44,900 

59,900 

65,900 

74,900 

31 

8.296 

50,600 

67,400 

74,100 

84,300 

3| 

8.946 

56,600 

75,500 

83,000 

94,400 

3J 

9.621 

63,100 

84,200 

92,600 

105,200 

3f 

10.321 

70,100 

93,500 

102,900 

116,900 

3f 

11.045 

77,700 

103,500 

113,900 

129,400 

33 

11.793 

85,700 

114,200 

125,600 

142,800 

4 

12.566 

94,200 

125,700 

138,200 

157,100 

41 

13.364 

103,400 

137,800 

151,600 

172,300 

41 

14.186 

113,000 

150,700 

165,800 

188,400 

43 

15.033 

123,300 

164,400 

180,800 

205,500 

4J 

15.904 

134,200 

178,900 

196,800 

223,700 

4| 

16.800 

145,700 

194,300 

213,700 

242,800 

4f 

17.721 

157,800 

210,400 

231,500 

263,000 

43 

18.665 

170,600 

227,500 

250,200 

284,400 

5 

19.635 

184,100 

245,400 

270,000 

306,800 

51 

20.629 

198,200 

264,300 

290,700 

330,400 

51 

21.648 

213,100 

284,100 

312,500 

355,200 

5| 

22.691 

228,700 

304,900 

335,400 

381,100 

5k 

23.758 

245,000 

326,700 

359,300 

408,300 

5f 

24.850 

262,100 

349,500 

384,400 

436,800 

5| 

25.967 

280,000 

373,300 

410.600 

466,600 

53 

27.109 

298,600 

398,200 

438,000 

497,700 

Bending    Moments   ot   Pins 


247 


BENDING  MOMENTS   OF  PINS.  —  {Continued. ) 


Moment  =    '   7>y. 


Diameter  ■= 


1MAM- 
KTBB    OF 

J'lN     IN 

Inches. 

A  i:i    \  OF 

1'IN   1N 

Squabb 

Inches. 

.Mo.MKNTs  in  In.  h  Pounds  pob 
Stb  luth  of 

Fibbb 

15,000  Lbs. 

2O,U(J0  Lbs. 

22,000  Lbs. 

25,000  Lbs. 

per 

per 

per 

per 

28.274 

Sq.    Inch. 

Sq. Inch. 

Sq.  Inch. 

406,500 

Sq.  Inch. 

6 

318,100 

424,100 

530,21  0 

&i 

29.465 

338,400 

451,200 

496,300 

564,01  0 

<H 

30.GS0 

359,500 

479,400 

527,300 

599,210 

6§ 

3L919 

381,500 

508.7(H) 

559,600 

635,900 

6J 

33.183 

4U4.4HO 

539,200 

593,100 

674,(  1  ii 

6j 

34.472 

428,200 

570.1MH) 

628,000 

713,700 

63 

35.785 

452,900 

603.900 

664,200 

754,800 

'J-1 

37.122 

478,500 

038.000 

701,800 

797. .'-Hi 

7 

38.485 

505,100 

673,500 

740,800 

84i;900 

7i 

39.871 

532,700 

710,200 

781,200 

887,800 

7i 

41.282 

561,200 

74-.200 

,000 

935,300 

n 

42.718 

590,700 

7-7.t300 

866,300 

984,500 

7h 

44.179 

621,300 

828,400 

911,200 

1,035.400 

•- 

45.664 

652,900 

870,500 

957,500 

1,1 188, 100 

7! 

47.173 

685,500 

914,000 

1.005,300 

1.142,500 

"i 

4*.707 

719,200 

958,900 

1,054,800 

1,198,700 

8 

50.265 

754,000 

1,005,300 

1,105,800 

1, 256,600 

81 

51.849 

789,900 

1.053,200 

1,158,500 

1.316,500 

N 

53.456 

826,900 

1.102.500 

1.212,800 

1.378,200 

*i 

."..-..088 

865,100 

1,153,400 

1,268,800 

1,441.800 

4 

56.745 

904,400 

1.2D5.800 

1,326,400 

1,507,300 

"; 

58.426 

944.900 

1,259.800 

1,385,800 

1  ..-.74.800 

8J 

GO.  132 

986,500 

1,315,400 

1,446,900 

1,644.200 

81 

61.862 

1,029,400 

1,372,500 

1,509,800 

1,715,700 

9 

63.617 

1.073,500 

1.431.400 

1. -.74. 500 

1,7S9,200 

»i 

65.397 

1.118,900 

1,491,900 

1. 641, 100 

1,864,800 

67.201 

1,165,500 

1,554.000 

1,709.400 

1.942,500 

69.029 

1.213,400 

1.617.900 

1,779,600 

2,022,300 

70.--  2 

1,262,600 

1,683,400 

1,851,800 

2,104,300 

9g 

72.760 

1,313,100 

1,750,800 

1,925,900 

2.188,500 

n 

74.662 

1,364,960 

1.M9.900 

2,001,900 

2,274,960 

H 

76.590 

1,418,100 

l.S90,800 

2.07: '.'100 

2,363,600 

10 

78. r-4 

1,472,600 

1,963,500 

2,159,900 

2.4.-4 ,400 

m 

82.-2 

1,585,91  n 

•-M14..-.00 

2,325,900 

2.143.100 

lOj 

86.59 

1,704,70  > 

2,273,000 

2.500,200 

2, 841, 200 

10| 

90.76 

1,829,400 

2,439,300 

2,683,200 

3,049,100 

11 

95  .as 

1,960,100 

2,613,400 

2,874,81  0 

3.266,800 

111 

99.40 

2,096,800 

2,795,700 

3.075,400 

3.494,800 

11* 

H»;;. -7 

2,239,700 

2,9*6,300 

3,284,800 

::.  732,800 

12 

113.10 

2,544,700 

3,3:  »2.:«  hi 

3,732,200 

4.241.200 

248 


The   Naval  Constructor 


TEES   AS    STRUTS. 


r  —  least  radius  of  gyration. 


Size  of 

Tee  en 

Inches. 

Length  in  Feet. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

Greatest  Safe  Load  in  Pounds  per  Square  luck  of  Section. 

4X4) 
r  =.85  S 

Hx  8J  ) 

r  =.73  ( 

3  x    3} 
r  =.62  i 

2ix  n  i 

r  =.54  ( 

81x211 

r  =.48  f 

2  x    2| 
r  =.41  j 

Ifxlfl 

r  =.36  J 

%H} 

r  =  .32  J 

llx  H  I 
r  =.30  J 

1  x    1( 
r  =.26  j 

16,280 
14,680 
13,670 
13,010 
12,600 
11,870 
11,130 
10,400 
10,000 
9,060 

12,110 
11,200 
10,210 
9,310 
8,500 
7,330 
6,310 
5,330 
4,780 
3,540 

9,640 
8,600 
7,390 
6,310 
5,330 
3,970 
2,960 
2,340 
2,070 
1,510 

7,610 
6,420 
5,060 
3,860 
2,960 
2,170 
1,660 
1,200 

5,840 
4,550 
3,190 
2,400 
1,910 
1,290 

4,280 
3,060 
2,210 
1,660 
1,200 

3,040 
2,250 
1,590 

2,330 

1,710 

1,840 
1,250 

1,430 

Special  Shackles 


249 


SHACKLES. 

For  most  purposes  in  ship  details  where  shackles  are  used,  it  is 
common  practice  to  order  the  shackles  given  in  Table  of  trade 
shackles,  suiting  the  size  to  the  chain,  wire  or  manila  rope  that 


SPECIAL  SHACKLES 


Tin.  HI. 

they  are  linked  with.  Where,  however,  special  cases  arise  in  deal- 
in?  with  exceptional  loads  the  size  of  the  shackle  and  pin  should 
be'accurately  calculated,  taking  care  that  the  widths  between  jaws 
and  across  the  bow  are  no  greater  than  necessary  to  take  the  con- 


250  The  Naval  Constructor 

nections,  as  these  dimensions  are  considered  as  the  beams  support- 
ing the  load  as  in  the  diagram. 

The  dimensions  are  required  of  a  shackle  to  take  a  working 
load  of  10  tons  (22,400  lbs.),  with  a  factor  of  safety  of  6  equal  to 
a  unit  stress  of  10,000  lbs.  It  is  assumed  that  the  pin  is  shipped 
in  a  pad-eye,  bearing  along  its  entire  length,  i.e.,  the  load  is  dis- 
tributed.    We  thus  have  the  case  of  a  beam  supported  at  the  ends 

.      Wl 
and  uniformly  loaded,  the  maximum  bending  moment  M  being  — • 

The  length  I  (3")  will  have  previously  been  determined  by  the 
bearing  value  given  in  designing  the  pad-eye.     Then, 

Wl      22,400  X3      D(Aft.     ,  ,        ,, 

—  — '—— =  8,400  inch-pounds  =  M. 

8  8 

The  moment  of  resistance  of  a  circular  section  (the  pin)  is  equal 

to  —  D3,  therefore  the  diameter  D  which  will  equal  this  bending 

32 
moment  (M)  just  figured  with  a  fibre  stress  of  10,000  lbs.  must  be, 

n_    ^l^d~_k3r        8,400 

D  ~  V  ]T  -  "  V  3582X10,000  =  204  inches- 

32  X/ 

The  diameter  of  the  wire  forming  the  bow  at  B  is  calculated  in 

a  similar  way,  noting  that  the  load  this  time  is  central,  but  the 

ends  of  the  beam  being  now  fixed,  we  have  the  same  formula  for 

WU 
the  maximum  bending  moment,  viz.,  — =-■    Assuming  that  it  has 

been  necessary  to  bow  the  shackle,  "  h  "  has  now  been  increased 
to  4  inches,  so  that 

Wh     22,400x4       110.A.     .  .        ,. 
=  — — =  11,200  inch-pounds  =  M, 

8  8 

and  applying  the  formula  for  a  circular  section  as  in  the  pin,  we 


have 


3/        11,200 
y  .0982  X  10, 


-==  2i  inches  diameter  at  B. 
000        i 


From  the  diameter  B  the  wire  may  be  tapered  to  A,  where  the 
sectional  area  need  only  be  such  as  will  resist  tension,  but  it  is 
usual  in  practice  to  increase  this  amount  by  25%,  owing  to  the  load 
at  times  becoming  eccentric,  thus  throwing  a  greater  stress  on  one 
leg. 

W      22,400  lbs.      nni  ,  acni    ■  00 

7"=ii)!oo(nbs:=2-24sq- in-  +25%=2-8s<i-  -• 

=  1.4  sq.  in.  per  leg. 
=  If  in.  diameter  at  A. 


Special   Shackles  251 

The  sectional  area  and  dimension  C  are  computed  by  consider- 
ing l2  the  length  of   beam  which  is  now  fixed  at  both  ends  and 

uniformly  loaded  when  M  is  equal  to  -j^-    The   dimensions   are 

calculated  as  in  the  foregoing,  observing  that  the  resistance  is  now 
for  a  rectangle,  and  the  bending  moment  will  consequently  equal 

AC* 


6 


xf. 


252  The  Naval  Constructor 


CHAPTER   IV. 

STANDARD    RIVETING,   U.  S.  NAVY. 

1.  All  rivet  holes  through  material  1  inch  or  more  in  thickness 
should  be  drilled,  or  if  punched  should  afterwards  be  reamed  to  fin- 
ished size. 

2.  In  cases  where  rivets  connect  plates  of  different  thickness 
the  size  of  rivet  indicated  for  the  greater  thickness  with  corre- 
sponding spacing  will  be  used  where  strength  is  required,  and 
that  indicated  for  the  lesser  thickness  where  water  tightness  is  a 
special  consideration,  always  provided  the  greater  thickness  is  not 
more  than  double  the  lesser. 

3.  Where  tap-rivets  must  be  used  they  should  be  J  inch  larger 
than  the  corresponding  ordinary  rivets  for  the  same  thickness, 
except  taps  into  heavy  castings  and  forgings  such  as  stem  and 
stern  posts,  which  should  be  \  inch  larger.  Where  strength  is 
required,  taps  should  not  penetrate  less  than  one  diameter,  and 
should  penetrate  1^  diameters  when  the  thickness  of  metal  will 
allow  it. 

4.  Where  the  spacing  given  in  Table  No.  3  cannot  be  followed 
exactly,  as  will  generally  be  the  case,  make  the  spacing  a  trifle 
closer  (as  necessary  with  heavier  plating)  and  a  trifle  further  apart 
(as  necessary  with  lighter  plating),  the  division  between  "  heavier" 
and  "  lighter""  plating  coming  at  7i-pound  plates  for  single  rivet- 
ing;  at  15-pound  plates  for  double  riveting  and  at  25-pound  plates 
for  treble  riveting. 

5.  Where  the  above  distinctions  are  considered  too  complicated 
for  yard  work,  the  general  rule  will  be  to  space  a  trifle  closer  in 
all  cases,  as  necessary  for  equal  spacing. 

6.  Where  strength  is  required  in  laps  and  butted  connections 
of  plating,  with  the  spacing  indicated,  single  riveting  is  suitable 
only  for  plating  under  12  £  pounds,  and  double  riveting  for  plating 
under  25  pounds.  For  maximum  strength  in  connections  of  plat- 
ing above  30  pounds  it  will  generally  be  found  that  quadruple 
riveting  is  required. 

Single  Straps. 

7.  Single  butt  straps  and  edge  strips,  when  single  or  double 
riveted,  should  be  the  same  thickness  as  the  plates  connected,  and 
where  the  plates  connected  are  of  different  thickness,  the  straps  or 
strips  should  be  of  the  same  thickness  as  the  lighter  plate.  Single 
butt  straps  when  treble  riveted  should  be  1^  times  the  thickness  of 
the  plates  they  connect. 


Standard    Riveting,    U.S.    Navy  253 

Double  Butt  Straps. 

8.  Double  butt  straps  should  not  be  used  for  water-tight  work, 
owing  to  the  difficulty  in  caulking.  They  may  be  used  to  advan- 
tage in  conditions  requiring  greal  strength  but  not  water-tightness. 
The  thickness  of  each  strap  should  be  £  the  thickness  of  plates 
connected  for  double  riveted  straps,  and  fj  the  thickness  for  treble 
riveted  straps.  The  spacing  of  rivets  in  rows  should  be  calculated. 
Size  of  rivets  for  double  butt  straps  as  follows  : 

For  plates  from  15  to  20  pounds,  exclusive,  j|  inch  rivets. 
»        "        "     20  to  25       "        inclusive,  j     "        " 
11        "      above  25  pounds,  see  Table  No.  1. 

Distance  between  Rows. 

0.  Centres  of  rivets  should  be  placed  not  less  than  If  times  the 
diameter  from  the  edges  of  plates  connected.  In  double  and  treble 
riveting  for  laps  and  single  straps,  the  distance  from  centre  to  centre 
of  rows  should  not  be  less  than  2£  diameters;  in  butt  laps  and 
double  butt  straps  the  distance  between  centres  of  rows  should  be 
not  less  than  3  diameters.  (Butt  laps  should  be  at  least  double 
riveted.)  For  zigzag  riveting  the  distance  between  centres  of  rows 
should  not  be  less  than  If  diameters  for  rivets  spaced  4  diameters 
apart  in  rows. 


254 


The  Naval   Constructor 


TABLE   I.  —  Diameter  of  Rivets. 


"Weight  of  Plates. 


For  Torpedo  Boat  Work. 
Up  to  3  pounds,  inclusive     .... 

3  pounds  to  6  pounds,  exclusive    .  . 

6  pounds  to  7\  pounds,  exclusive  . 

7 1  pounds  to  9  pounds,  exclusive  .  . 

9  pounds  to  1 1  pounds,  exclusive  .  . 

11  pounds  to  13  pounds,  exclusive  .  . 

For  Ship  Work. 

Up  to  3  pounds,  exclusive    .... 

3  pounds  to  6  pounds,  exclusive    .     . 

6  pounds,  inclusive,  to  8  pounds,  exclusive 

8  pounds,  inclusive,  to  13  pounds,  exclusive 
13  pounds,  inclusive,  to  20  pounds,  exclusive 
20  pounds,  inclusive,  to  30  pounds,  exclusive 
30  pounds,  inclusive,  to  40  pounds,  exclusive 
40  pounds,  inclusive,  to  51  pounds,  exclusive 
51  pounds  and  above 


fa  s 

«?fa 
H  %  > 

"^  S3 

a  ° 


In. 


I 


5 
T6 


T6 


£ 

I 


1 

n 


at 

«  y 

fa  fa  ai 

£  £  H 

fa£  j 


In. 


_9_ 
32" 

1  1 
32" 

7 
T6 

1 

2 


9 
T"6~ 

1  1 
T6 


9 

J? 


_9_ 
16 

11 
16 

13 

16 

15 
1  6 


1A- 


x32 
1  11 


Breadth   ol    Laps   and   Straps 


255 


TABLE    II. —Breadth   of  Laps  and  Straps. 


ITKM. 


Breadth  of  laps  for  single  riveting 


••    double  chain  riveting 


zigzag  riveting 


Diam- 
eters 


double  riveted  butt  laps 

laps  for  treble  riveting        

treble  riveted  butt  laps  in  outside  plating 
edge  strip  for  single  riveting  .... 
edge  strip  for  double  riveting  .... 
butt  strap  for  double  riveting  .... 
butt  strap  for  treble  riveting  ..... 
double  butt  strap,  double  riveted  .  . 
double  butt  strap,  treble  riveted  ... 


■>\ 


5 


«* 


n 


6i 

1H 

16* 
12$ 

18§ 


256 


The  Naval  Constructor 


TABLE    III.  —  Spacing  of  Rivets. 


Pitch  ix 
Diam- 
eters. 


3| 
4 

4i 


4i 


Single  riveted  butt  laps  and  butt  straps 

Double  riveted  butt  laps  and  butt  straps 

Treble  riveted  butt  laps 

Treble  riveted  butt  straps  with  alternate  rivets  in  third 
row  omitted 

'All  longitudinal  seams  of  plating  required  to  be  water- 
tight      

Connections  of  transverse  frames  not  water-tight  to 

outside  plating 8 

Connections  of  deck  plating  to  beams,  of  non-water- 
tight longitudinals  to  outside  plating,  of  the  angles 
and  stiff eners  to  bulkheads  when  entirely  above 
the  water  line,  and  in  general  where  special 
strength  is  not  required 

Connections  of  floor  plates,  brackets,  lightened  inter- 
costals,  etc.,  to  clips  and  angles,  of  the  vertical 
keel  angles  to  the  flat  and  vertical  keel  plates  and 
to  the  flat  keelson  plates  beyond  the  limits  of 
double  bottom,  provided  water-tightness  is  not 
required 

Connections  of  angles  and  other  stiffeners  to  bulkheads 
at  or  below  the  water  line,  of  boiler  and  engine 
bearings  and  foundations  in  general 6 

Connections  of  inner  bottom  plating  to  all  frames  and 

longitudinals 5 

Connections  of  angles  of  water-tight  frames  and  longi- 
tudinals to  all  plating,  and  in  general  where  water- 
tightness  is  required  between  shapes  and  plates    . 

Angles  and  other  stiffeners  to  bulkheads  forming  sup- 
ports to  turrets,  barbettes,  connections  of  armor 
shelf  angles  to  plating,  etc 

Connections  between  staple  angles  of  water-tight  floors 
and  the  floor  plates 

In  special  cases  of  intercostals,  beam  ends,  etc.,  where 
strength  is  required  in  connections  of  limited 
strength  and  in  all  other  exceptional  cases,  spac- 
ing to  be  as  required  by  circumstances,  except  that 
the  rivets  in  the  same  line  should  never  be  less 
than 


41 

*2 


Reduction   of  Diameters   to   Inches 


207 


09 
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258 


The   Naval   Constructor 


TABLE  V.  —  Combination  Table  for  Ship  Work. 


. 

H 

H 

w 

IDTHS   OF 

W 

(5 

W 

O 
i— i 

Brkadth  of  Laps. 

Strips  &  Sin- 

H 
< 

Ph 

—    /: 

Q  « 

5 

gle  Straps. 

c 

o 

- 

W> 

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45 

fa 

C 

as  S 

83 

3  tJC 

Q.2 

P 

bo  si 

0>  X 

>  ft 

si 
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3 

o 

s 

P 

S  0) 
1— 1 

2  > 

"55 

P 

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H 

0>  +3 

P 

gffl 

—  > 

0)  o> 

Pounds 

i    as 

*s  ~  a  - 

per 

Soso 

In. 

In. 

111. 

In. 

In. 

In. 

Tn. 

In. 

In 

in. 

III. 

Sq.  Foot 

l 

4 

9 
32 

1  3 
16 

iA 

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1  § 

1  8 

Up  to  3  Ex. 

Up  to  2 

2TV 

I-9- 

xl  6 

2T56 

9  " 

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4  1 

*  8 

3-0     'l 

2-5 

3 
8 

7 
16 

1-3- 

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1  z 

»A 

2A 

8tV 

2TV 

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0-8    " 

5-7 

1 

2 

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1  6 

1  5. 

1  8 

21 

2| 

4  i 

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8* 

4  4 

*  8 

81 

5f 

81 

8-13  '; 

7-11 

5 

8 

1  1 
16 

9   3 

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Q   5 
d  8 

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5-3- 

"16 

m 

513 

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4-1- 

7_3_ 

'  16 

i«A 

13-20  " 

11-15 

3 
4 

13 

16 

9  7 

ZT6 

4_5_ 
*16 

8* 

"16 

M 

*tt 

41 

8f 

12  | 

20-30  " 

15-24 

7 
8 

1  5 
T6 

•   • 

5 

4  § 

*  8 

*A 

5i 

8A 

5  1 

ioa 

i*A 

30-40  " 

24-32 

1 

1A 

•   • 

B| 

5 

8i 

6i 

»i 

<H 

111 

16  § 

40-51  " 

32-41 

1* 

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7 

10  | 

7A 

WH 

18T9e 

51  &  over 

41  &  | 

over ) 

n 

Hi 

10A 

71  3 
'  1  6 

Ht96 

81 

14  | 

20  | 

Llovd's   Countersinks 


259 


tn 
M 

- 

O 

u 

en 
Q 

o 


TORM  OF  RIVET  TO  BE  USEJ  IN  OUTSIDE 
PLATING. 


Ad- 


J 


-1  . 1  2 .7      —  • 


-1.6(2 •• 


-xl - 


THE  TAPERED  NECK  OF  RIVET  TO  e£  OF  SUITABLE 
LENGTH  IN  RELATION  TO  THE  THICKNESS  OF  PLATE 
IN  WHICH   IT   IS   INTENDED  TO   BE   USED. 

Fig. 117. 


'-'-, 


260 


The   Naval   Constructor 


LLOYD'S    RIVETING 
Showing  Diameters  and  Spacing  of  Rivets  and 


Thickness  of  plates  . 

Diameter  of  rivets 

Breadth  of  treble  riveted  straps  in  inches    .    .    . 

"        "  double  riveted  straps  in  inches    .    .     . 

44        44  quadruple  riveted  butt  laps  in  inches 

44        44  treble  riveted  butt  laps  in  inches    .    . 

44        44  double  riveted  butt  laps  in  inches  .    . 

44        44  treble  riveted  edge  laps  in  inches    .    . 

44        44  double  riveted  edge  laps  in  inches  .     . 

44        44  single  riveted  edge  laps  in  inches    .    . 


o 

f3Jdia. 

o 

6 

hf 

c.  to  c. 

4  dia. 

c.  to  c. 

DC 

4J  dia. 

c.  to  c. 

5  dia. 

5 

— 

c.  to  c. 
7  dia. 

X 

c.  to  c. 

In  f  butts  of  outside  plating,  and  of  upper,  spar  and  middle  deck 
stringers  and  tbe  stringers  of  bridge  decks  wLich  exceed  one-third  the 
length  of  the  vessel  amidships    (except  quadruple  riveted  butt  laps). 

In  quadruple  riveted  butt  laps  ;  butts  of  deck  plating,  margin  plates, 
girders,  lower  deck  and  hold  stringers,  tie  plates,  floor  plates,  and 
stringer  plates  on  other  deck  erections  ;  also  butts  and  edges  of  inner 
bottom  plating. 

In  *  edges  of  outside  plating  (forward  and  aft),  gunwale  angle  bars, 
margin  plate  angles,  edges  and  butts  of  bulkhead  plating. 

In  flat  keel  angles,  bulkhead  frames  where  caulked,  butts  and  edges 
of  mast  plates,  and  deck  plating  to  beams  where  single  flange  beams 
are  fitted  to  alternate  frames. 

In  *  frames,  reversed  frames,  floors,  keelsons,  beam  angles,  deck  and 
bold  stringer  angles,  face  angles  on  web  frames  and  side  stringers, 
bulkhead  stiffeners,  longitudinal  angles  on  continuous  girders,  verti- 
cal angles  connecting  floors  and  girders  and  deck  plating  to  beams 
except  where  single   flange  beams  are  fitted  to  alternate  frames. 


//       // 


H 


•J4 


-S-       6     X-     7 

a 

4 


■H 


2i 


'i1 

°8 


4* 


9f 


2§ 


qa 

^4 


5i 


t  In  butts  connected  by  single  butt  straps  alternate  rivets  may  be  omitted 
in  the  back  row  of  treble  riveting  when  the  plating  number  is  20,000  and  un- 
der ;  when  above  this  number,  the  rivets  in  tbe  back  row  are  not  to  be 
more  than  5  to  5J  diameters  apart  from  centre  to  centre.  All  overlapped 
butts  are  to  have  complete  rows  of  rivets. 

*  When  the  rule  frame  spacing  is  2G  inches  or  above,  the  rivets  in  the 
edges  of  outside  plating  (forward  and  aft)  are  not  to  exceed  4  diameters 
apart  from  centre  to  centre,  and  the  rivets  attaching  the  outside  plating 
to  frames  are  to  be  spaced  not  more  than  6  diameters  apart  from  centre 
to  centre. 

In  deep  water  ballast  tanks  above  the  level  of  inner  bottom,  and  in  fore 
and  after  peak  water  ballast  tanks,  tbe  rivets  through  frames  and  outside 
plating  are  to  be  spaced  not  more  than  6  diameters  apart  from  centre  to 
centre. 

Before  the  three-fifths  length  of  a  steamer  having  a  tonnage  coefficient  of 
.78,  or  having  a  full  form  at  the  fore  part,  the  rivets  in  the  landing  edges  of 
the  strakes  of  plating  forming  the  flat  of  the  bottom  to  be  spaced  not  more 
than  4  diameters  apart  from  centre  to  centre.  The  rivets  in  the  plating  and 
frames  in  way  of  the  same  to  be  spaced  not  more  than  5J  diameters  apart 
from  centre  to  centre. 

Rivets  to  be  \  of  an  inch  larger  in  diameter  in  the  stem,  stern  frame,  and 
keel,  but  in  no  case  need  these  exceed  \\"  in  diameter,  and  to  be  spaced  5 
diameters  apart  from  centre  to  centre.  In  single  screw  steamers  above  350 
feet  in  length,  the  after  lengths  of  shell  plating  are  to  be  connected  to  the 
portion  of  the  stern  frame  below  the  boss  with  3  rows  of  rivets. 

Rivets  in  side  plate  rudders  to  be  of  not  less  size  than  those  required  for 
the  upper  edge  of  garboard  strake  amidships,  and  to  be  spaced  not  more  than 


Lloyd's    Riveting  Table 


201 


TABLE,  1903. 

Breadths  of  Straps^  Butt  Laps,  and  Edge  Laps, 


II 

t 

5 

2| 
3 

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"a 

5  diameters  from  centre  to  centre.  The  rudder  plates  are  to  be  countersunk 
and  thu  rivets  are  to  have  full  heads  and  points. 

Rivets  in  single  plate  rudders  are  to  be  of  not  less  size  than  required  for 
attaching  the  outside  plating  to  the  stern  frame,  and  spaced  not  more  than 
5  diameters  apart  from  centre  to  centre.  The  rivet  holes  are  to  be  counter- 
sunk both  in  rudder  plates  and  the  arms,  and  the  rivets  are  to  have  full 
heads  and  points. 

Rivets  in  the  edges  of  deck  plating  are  to  be  spaced  not  more  than  4  to  4.^ 
diai iK-ters  apart  from  centre  to  centre. 

In  single  riveted  seams  one  frame  rivet  is  to  be  fitted  through  the  landing 
edges  at  each  frame.  In  double  riveted  seams  one  frame  rivet  is  to  be  fitted 
through  the  landing  edges  at  each  frame,  except  where  the  frames  or  the 
edges  of  the  <>utsiile  plating  are  joggled  when  two  rivets  are  to  lie  fitted.  In 
treble  riveted  Beams  two  frame  rivets  (the  upper  and  lower)  are  to  befitted 
through  the  landing  edges  at  each  frame. 

Where  the  fore  and  aft  Mange  of  the  frame  does  not  exceed  3  inches,  the 
rivets  attaching  the  outside  plating  thereto  should  not  exceed  g  inch  in 
diameter,  and  where  it  is  3A  inches  wide,  they  should  not  exceed  1  inch  in 
diameter. 

There  are  to  be  at  least  four  rivets  in  each  flange  of  the  angle  bars  be- 
tween the  frames  which  connect  the  stringer  plates  and  intercostal  plates 
to  the  outside  plating.  Where  the  Frames  are  spaced  less  than  29  inches 
apart,  and  where  the  spacing  i-  29  inches  and  not  more  than  .7J  inches  there 
are  to  be  five  rivets  in  each  flange. 

The  rivets  in  the  beam  knees  are  to  he  in  number  and  size  as  required. 

The  rivets  in  the  vertical  angles  connecting  floors  and  outside  brackets  to 
margin  plates  are  to  he  in  number  and  size  as  required. 

The  rivets  in  the  connecting  -traps  for  Web  (rallies  and  side  stringers  are 
to  be  in  number  and  Bize  as  required. 


262 


The   Naval   Constructor 


STANDARD    RIVETS. 


(See  Table  Opposite.) 


COUNTERSINK  OR  PLUG  HEADS'  PAN  HEAD  BUTTON  HEAD 

CLASS  A       ,   CLASS  B   ,     ,  CLASS  A        CLASS  B  CLASS  A        CLASS  B 

-K-g »! 

m 


TEMPLATE 
FOR 
COUNTERSINK 


BUTTON  OR  SNAP   HAMMERED  OR  MASHED 
POINT  POINT 


Figs.  118-129. 


Standard    Rivets 


263 


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264 


The  Naval   Constructor 


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266 


The   Naval   Constructor 


a 

EH 

* 


CO 

M 

n 

cc 


Z 

M 

H 
W 
> 

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W 

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Cj> 

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ti 
Eh 
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Double 
Straps 
Treble 
Rivet. 

fa 
o 

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rIMHH 

"3  ®  d 

X 

CO 

t-  « <o  o  o i  »  o  -t  o  «  f )  »  li  :i 

HOHoaoooooooot-i-i- 

Ratio  of  Stki 
of  Riveting  to  Stj 

Solid  Plate  = 

i— i  -w    • 

-o   v  — 
0>  t»  03 

.     .  t-  CI  LO  00  IS  O'OCOH  1-  IN  LO  (N  Li  r-  I p  «  00  »  -fi 

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S3 


STRENGTH    OF    RIVETING   IN    SHIPS.  —  Table  II.    Butt  Riveting. 

Strength   of  Riveting  in    Ships           26 

M 

< 
0 

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y 

u 

- 

<J 

DO 

OB 
V 

r. 

r. 

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f. 

r. 

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268 


The   Naval   Constructor 


Five  Tiers 

of 

Beams. 

pamqiuoQ 

•3uiuru.ij[  jo 
Suipubg  oj  8uq; 

• 

s 

fa 
-4 

3 

fa 

0 

M 
Mi 

o 

1—1 

fa 

fa 

p 
C 
02 

fa 
fa 
fa 

O 

M 

m 
tf. 

fa 
fa 
H 
02 

Four  Tiers 

of 

Beams. 

•SS9JJg 

pauiqmoQ 

o  o  o    •    • 

....••■.  Cj  !>•  i— i      m      # 

•SupOTBJ^  JO 

Sutpuog   oj  end 

Three  Tiers 

of 

Beams. 

"SS8.HS 

peniquiof) 

•Suuuktj  jo 
Sinpuag;  oj    9U(i 

O  O  GO 

Two  Tiers 
of 

Beams. 

•SS9.IJS 

pGuiquioQ 

.  C5  O  CM  t— I  CO  OS 

'SmxmeijL  jo 
Strrptrag  oj  ouq 

.      .  T-"  •<*  00  CM  CO  fc- 

One  Tier 

of 
Beams. 

*SS9JJS 

pauiquioo 

'SnimtUji  jo 
Sinpuea    oj  9U(X 

Due  to  Main 

Sheering 

Forces. 

•dwj  o§p3 
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3AIH  ^o   ouiovag 

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ococoo:conco»-oc>ooco 

OOH00<*'*OMCCOrHO'* 

c^cocococococ^'*co-<#'*>-o-^ 

Size  of 

Rivet    in 

Inches. 

t-  CM         t-                      CM                      t~ 

COH         CO                     CD^^^GO 

oao^o^    ^    i   o  -    ~    -  i-H  - 

1—1                                            T— 1 

2.- 

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IKStKaOVTxISKI 

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CO»NOONHJ)OCCOOO_ 

r-TcoTo~t^T-rio  o'-^ocTco'ao" 

i-i  i—l  CM  CM  CM  CO  CO 

13 

•xaaj  si 

9 

OOOOOOOOOOOOO 

ooooo*oooo»ooioo 

HhC^OICOCO^^OOCOCD^ 

Ordered   Lengths  of  Rivets 


269 


in 

w 
> 

M 
« 

Cm 
O 

O 

H 

Q 

H 

s 

H 
A 
« 
O 


^ 


c 

< 

u 

:• 

c 

,: 

a.      < 

LU         <; 

<i       u 
X 


LU 

I 
I- 

u 

a 

c 
1- 

z 

LU 
< 


-I 
0- 

< 

x 

m 


( 

\ 

H 

O 
O 

u. 

a. 
O 
cr 

1 

CO 

J 

a. 

Ul 

z 
o 

t- 

a. 

U. 

1 

</> 

O 

u. 

in 

u. 

o 

(r 

CO 

o 

a. 

n- 

CO 

i. 

O 
a 

LU 

Q 
LU 

O 

i 

_l 

h- 

(1 

< 

7 

LU 

O 
(0 

O 

> 

h- 

LU 
03 

a. 

1- 

3 

o 

O 

o 

< 

LU 

Z 

o 

3 
CO 

I 

O 

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s 

s 
< 
5 

O 

z 

o 

o 

Ul 

BC 

IT 

» 

-1 

u. 

LU   _ 

L 

270 


The   Naval   Constructor 


STRENGTH   OF 


Table  IV.— 


H 
02 

02 

H    . 

>H 

r       « 

H 

J 

(i). 

100 
150 
200 
250 
300 
350 
400 
450 
500 
550 
600 
650 
700 

-A 

M 

H 

•«j 

02  " 

M 

a 
(0. 

6 
20 

7 

55 

280 

10 
2  0 

1  1 
20 

12 
20 

13 
20 

14 
20 

IS 

2  0 

16 
20 

17 

50 

18 
50 

19 
20 

30 

m 

«   3D 

&  a? 

2  O 
0  izi 

5* 

-4 

20 
21 
22 
23 
24 
24 
25 
26 
27 
28 
29 
30 
31 

Rivet  in 
Frames  and 
Outside 
Plating. 

One  Tier  of  Beams. 

Two  Tiers  of  Beams. 

CO 

+s 

> 

'K.S 

u  s 
©i3 

05   - 
5 

5 

8 

3 
i 

(I 

5 

u 

it 

it 

1 
II 

II 

II 

ii 

CO 
«4-C    <E 

a-S 

CS   02 

so 

CD 

C   = 

"li 

CO  > 

4.50 

5.25 

it 

6.25 

it 

ii 

it 

7.00 

6.50 
ii 

6.00 

6.75 
ii 

Frame. 

Reverse 
Frame. 

cp 

BE    — 

s  ° 
©.£ 

«8 

■>-<  cS 
as  5 

30    o* 

cc 

.93. 
1.50 
3.06 
2.83 
3.30 

Frame. 

Reverse 
Frame. 

3> 
g"3 

30  CT 

a; -03 

-u 

CC 

4.30 
4.10 
4.60 
4.80 
4.80 
4.00 

(«*l). 

Inches. 

Inches. 

Inches. 

Inches. 

.687 

.812 

ii 

.937 

ii 

ii 

1.062 

a 

ii 

k 

1.187 
i< 

*-2~X  --2~X  20 

3  X3  X20 
4oX3  Xgg 

5  X3  X50 

6  X3iX2% 

None. 

-5T^5       50 

Alter- 
nately. 
1  X 3  X 20 

5  X3  X^jj 

•'2  X3o  X  20" 

3oX3  X20 
4^X3  X57o 

^*2  X*>2  X  20 

6  X3iX59o- 

Oo"  X  0~2  X  2  0" 

Tiv^lv  10 

3  X-5X20 

3  X3  X50 

4  X3jX^s 

O    X  ^2  X  2 <J 
D2XO2X2O 

7  X  3o  X  2~o~ 

Strength  of  Riveting  in  Ships  271 


RIVETING    IN    SHIPS. 

Frame  Riveting. 


Three  Tiers  •>[• 
Bkam>. 

FOUB  Tiers  OB 

Beams. 

I'l\  1.  TlEBS  «il 

Be  \  m- 

Frame. 

Reverse 

Frame. 

Stress  in  Tons  per 
Square  Inch. 

Frame. 

Reverse 
Frame. 

Si  ivss  in  Tuns  per 
Square  Inch. 

Frame. 

?2 

U    - 

Stress  111  Tons  per 
Square  lneli. 

Inches. 

Indies. 

Inches. 

Inches. 

I  aches. 

05X*%X  Jo 

6  X3*X5o 

7  X3jXz8 

i  ■  Hx& 

4*x3*X5g 
4^X4  X5g 

6.90 
6.70 
5.55 

8x3ix3Jxiil 

8x35X05X30 
8X4  X4  X23 

N 1  >ne. 
11 

4X4X2§ 
Alter- 
nately. 

5.90 
5.55 
6.62 



.... 

•  • 

9X4X4X38 
9x4x4x2g 

None 

6.15 
6.00 

272 


The   Naval   Constructor 


SHEARING   AND    BEARING 

All  Dimensions 


Diameter  ok 
Rivet  (In.). 

Area 

in  Sq. 

In. 

.1104 

.1963 

.3068 

.4418 

.6013 

.7854 

Single 

Shear  at 

6,000  Lbs. 

Bearing  Value  for 

i 

5 

1  6 

1 

7 
16 

Fraction. 

Decimal. 
.375 
.500 
.625 

.750 

.875 

1.000 

3 

8~ 

1 

2 

5 

8 

3. 
4 

7 
8 

1 

660 
1,180 
1,840 
2,650 
3,610 
4,710 

1,130 
1,500 
1,880 

1.410 

1,690 

2,630 

1,880 
2,340 
2,810 

2,250 
2,810 
3,380 
3,940 

3,280 
3,940 
4,590 

5,250 

2,250 
2,630 
3,000 

3,280 
3,750 

4,500 

Diameter  of 
Kivet  (In.). 

Area 

ix  Sq. 

In. 

.1104 

.1963 

.3068 

.4418 

.6013 

.7854 

Single 

Shear  at 

7,500  Lbs. 

Bearing  Value  for 

i 

4 

5 
16 

1 

7 
1  6 

Fraction. 

Decimal. 

i 

5 
5 

3 

4 

7 
8 

1 

.375 

.500 
.625 
.750 
.875 
1.000 

830 
1,470 
2,300 
3,310 

4,510 
5,890 

1,410 

1,880 
2,340 

1,760 

2,110 

•         •         • 

3,280 

2,340 
2,930 

3,520 

2,810 
3,520 
4,220 
4,920 

4,100 
4,920 

5,740 
6,560 

2,810 
3,280 
3,750 

4,100 
4,690 

5,620 

Diameter  of 
Rivet  (In.). 

Area 

in  Sq. 

In. 

Single 
Shear  at 
10,000  Lbs. 

Bearing  Value  for 

i 

4 

5 

16 

a. 

8 

7 
16 

Fraction 

Decimal. 

1 
I 

5 

8 

3 
I 

7 
8 

1 

.375 
.500 
.625 
.750 
.875 
1.000 

.1104 
.1963 
.3068 
.4418 
.6013 
.7854 

1,100 
1,960 
3,070 
4,420 
6,010 
7.850 

1,880 
2,500 
3,130 

2,340 

2,810 

•         •         • 

4.380 

3,130 
3,910 
4,690 

3,750 
4,690 
5,630 
6,570 

5,470 
6,500 
7,660 
8,750 

3,750 
4,380 
5,000 

5,470 
6,250 

7,500 

Diameter  of 
Rivet  (In.). 

Area 

in  Sq. 

In. 

Single 
Shear  at 
12,000  Lbs. 

Bearing  Value  for 

i 

4 

5 
16 

8 

7 
16 

Fraction. 

3 

8 

1 

5 

8 

3 
4 

7 
1 

Decimal. 
.375 
.500 
.625 
.750 
.875 
1.000 

.1104 
.1963 
.3068 
.4418 
.6013 
.7854 

1,320 
2,360 
3,680 
5,300 
7,220 
9,430 

2,350 
3,130 
3,910 

2,930 

3,520 

•         •         • 

5,470 

3,910 

4,880 
5,860 

4,690 
5,860 
7,030 

8,210 

6,840 

8,210 

9,580 

10,940 

4,690 
5,470 
6,250 

6,840 
7,820 

9,380 

In  above  tables  all  bearing  values  above  or  to  right  of  upper  zigzag  lines 
are  greater  than  double  shear.    Values  between  upper  and  lower  zigzag 


Shearing  and   Bearing   Value   of  Rivets      273 


VALUE    OF    RIVETS. 
in  Inch]  s. 


Different  Thicknesses  01   Plate  is  In    \.t  12,000  Lbs.  per  Sq.  In. 

h 

9 

f 

i  i 

1 

10 

t 

1 

3,000 
3,750 

4,220 

4.090 
5,630 

6,190 

•     • 

6,750 

7.880  ' 

4,500 
5,250 
6,000 

5,160 

5.910 
6,750 

8,530 

0.750 

9,190 
10,500 

9,840 
11,250 

12,000 

6,560 

7.500 

7.220 
8,250 

9,000 

Different  Thickness]  a  of  Pi  lte  in  In.  at  15,000 Lbs.  per  Sc/.  In. 

\ 

9 
16 

§ 

1 1 

3 

4 

1  3 
1  0 

1 

16 

1 

3.7 
4.090 

5.280 

5,860 

7.030 

7.720 
9.030 

8.410 
9,850 

5.03(1 
6,560 
7,500 

0.33d 
7.380 
8.440 

10,07i  • 
12.190 

11.480 
13,130 

12,300 
14.000 

15.000 

8,200 
9,380 

10.310 

11,250 

Different  Tim  KNE8SE8  of  Plate  en  In.  at  20.000  Lbs.  per  Sq.  In. 

h 

9 

l  6 

§ 

1 1 

16 

i 

4 

1  3 

1  6 

7 

8 

1  5 
1  6 

1 

5,000 
6,250 

.     .     . 

7,030 

7,810 

9.380 

10.310 
12,030 

11,250 
13,130 

7,500 
8,750 

10. ( 

8.440 

9.. Mo 

11,250 

14,220 

10.250 

15,310 

17.500 

16,410 

18,75i) 

20.000 

10,940 

12.5(10 

13.7-"." 

15.000 

Different  Thicknesses  <>f  Plate  in  In*,  at  25,000  Lbs.  per  Sq.  I>\ 

i 

To 

1 

l  l 
T5 

2 

4 

1  :i 

1  0 

I 

1  5 
1  8 

1 

6,250 

7.810 

8,790 

9.77H 
11.720 

12,890 
16,040 

14,060 
16,410 

9,380 

in.  940 
12,600 

10,550 
12.310 
14,060 

17,770 
20,320 

19,140 
21,880 

l">.510 
23.440 

26,000 

13.07(1 
15.03,0 

17,190 

18.750 

lines  are  less  than  double  and  greater  than  Bingle  shear.    Values  helow 
to  left  of  lower  zigzag  linos  are  less  than  single  Bftear. 


and 


Section  III. 

DETAILS,    STRUCTURAL. 


KEELS. 

Ix  steel  ships  the  keel  is  invariably  one  of  the  three  forms  of  bar, 
flat  plate  or  side  bar,  thefirsl  and  third  being  almost  entirely  su- 
perseded by  the  flat  plate  type 
which  is  on  all  points  a  much 
better  method  of  construction 
than  the  others,  besides  having 
the  ureat  advantage  of  saving 
from  6  to  12  inches  of  draft,  there- 
by increasing  the  dead  weight 
carrying  capacity  from  about  15  Fic 

to  1,500  tons   respectively   on   a 

given  immersion.     Bar  keels  should  have  no  place  in  modern  ship 
construction,  unless  when  required  for  rubbing  purposes  only. 


Bar  Keels. 

These  should  be  made  of  rolled  steel  universal  bar  in  preference 
to  the  old-fashioned  scrap  iron  forgings  and  scarphed  together  in 
long  lengths  by  right  and  left-handed  scarphs.  The  scarphs  are 
mostly  made  nine  times  the  thickness  of  the  bar  in  length,  and  the 
jog,  or  check,  and  point  should  be  one  fourth  the  thickness. 
Scarphs  of  keel  should  be  close  fitting  and  for  that  reason  must  be 
machined,  the  connection  holes  for  rivets  are  drilled,  and  in  addi- 
tion a  few  holes,  about  one  third  the  number  of  regular  ones,  should 


A 


x 


o      o  J  •  o       o   *"o       o]      O       O       J 

D         O         JO         O.O  O     •'  O         O         0| 

I  f  I     I 


TACK  RIVETS 

Fig.  133. 

be  drilled  of  smaller  diameter,  but  countersunk  on  both  sides,  for 
tacking  the  various  lengths  together  before  erecting  and  riveting 
the  garboard  st  rakes.  Care  should  be  taken  that  these  scarphs  are 
shifted  well  clear  of  the  garboard  strake  and  centre  keelson  butts 
and  that  the  joints  of  scarphs  are  caulked  watertight. 

275 


276 


The   Naval   Constructor 


The  diameter  of  the  rivets  should  be  in  accordance  with  the  re- 
quirements of  the  riveting  tables  given  on  p.  260,  and  staggered 
as  shown.  The  vertical  spacing  requires  special  care  in  keeping 
clear  of  the  radius  of  garboard  plate  and  also  the  caulking  edge  of 
same  at  bottom,  which  is  raised  about  half  an  inch  from  lower  edge 
of  bar.  For  this  reason  it  is  advisable  to  set  off  the  bar  full 
size,  drawing  in  the  flanges  of  garboards  before  fixing  on  centres 
of  rivet  holes. 

Flat  Plate  Keels. 

Keels  of  this  type  are  made  of  a  thick  plate  forming  the  bottom 
member  of  a  girder  of  which  the  centre  keelson  is  the  web.  The 
forms  mostly  in  use  are  shown  by  the  Figs.  134  and  135.     Fig.  136 


Fig.  134. 

shows  a  very  efficient  and  economical  form  of  flat  plate  keel  and 
centre  keelson  devised  by  the  author  and  designed  with  a  struc- 
tural /section  for  small  and  moderate  sized  vessels  with  ordinary 
floor  construction.  Where  a  suitable  I  section  is  not  obtainable 
the  same  construction  may  be  retained  with  advantage  with  built- 
up  section. 

The  flat  plate  keel  should  always  be  arranged  as  an  inside  strake, 
as  by  so  doing  the  keel  and  its  sister  member  may  be  laid  on  the 


Fig.  135. 

keel  blocks  right  away  without  anticipating  linering  in  addition  to 
making  a  more  solid  job  and  saving  a  small  amount  of  draught. 
It  is  a  fallacy  to  place  it  outside  with  the  intention  of  disturbing 


Stems 


277 


only  one  plate  in  the  event  of  damage  —  a  remote  contingency 
which  should  not  be  allowed  to  interfere  with  good  construction. 

Where  a  doubling  is  required  by  the  classification  societies1  rules 
it  will  be  found  advantageous,  where  practicable,  to  increase  the 
plate  keel  to  a  sectional 
area  equivalent  to  that  of 
the  keel  and  doubling,  and 
if  double  but 'strap  be  re- 
quired, the  inside  one  may 
be  fitted  in  two  pieces. 

Scantlings  and  riveting 
will  be  as  specified  or  to 
rule  requirements. 

At  the  forward  and  after 
ends  the  keel  plate  must 
efficiently  incorporate  with 
the  stem  and  stern  frame 
respectively,  a  short 
"breeches"  plate  being 
usually  worked  for  this 
purpose.  In  small  con- 
struction a  "spoon"  plate  is  welded  to  the  bottom  of  stem  bar 
in  lieu  of  the  short  plate  referred  to,  and  a  similar  plate  of 
"gutter"  form  welded  to  stern  frame. 


Fig.  13G. 


STEMS. 

The  remarks  on  bar  keels  apply  equally  as  regards  details  to 
stems.      The  classification  societies'  rules  allow  a  reduction  in 


-H- 


STEM. 
BEARDING  LINE 


MLO.  ]/j    BREADTH   OF   FLAT  OF   KEEL 
/  STEM   OF   UNIVERSAL    BAR 

T—  -r / 


3.-— — " 

137. 


278  The   Naval   Constructor 


sectional  area  at  stem  heads,  but  as  the  practice  is  now  to  make  the 
stem  from  universal  rolled  bar,  it  will  prove  no  economy  to  taper 
it.  The  usual  method  of  connecting  lower  part  of  stem  to  keel 
plate  are  shown  by  Fig.  137.  In  straight  stems  the  profile  line 
should  be  cambered  about  §"  to  §"  from  where  it  joins  the  fore- 
foot curve  to  stem  head,  to  guard  against  the  illusion  of  the  contour 
line  appearing  hollow. 

STERN   FRAME. 

These  frames  are  mostly  forged  or  cast  in  steel  in  one  piece  for 
small  and  moderate  sized  steamers,  and  in  two  or  more  parts  for 
the  larger  vessels.  As  in  the  case  of  stems,  bar  keels,  etc.,  the 
scantlings  are  determined  from  the  corresponding  numeral  of  the 
societies'  rules  to  which  the  ship  is  being  constructed.  The  two 
posts  comprising  the  stern  frame,  viz.,  rudder  and  body  posts  with 
the  joining  arch,  are  of  similar  scantlings,  but  the  keel  piece  con- 
necting the  posts  at  bottom  while  of  the  same  sectional  area  as  the 
posts,  is  flattened  out  to  allow  of  the  keel  line  being  curved 
upwards  to  the  clump  for  keel  pintle  bearing  of  rudder  for  pro- 
tection to  the  latter  in  the  event  of  grounding. 

Gudgeons  are  forged  on  the  rudder  post  of  frame  from  4  to  b\ 
feet  apart  to  take  the  pintles  ;  one,  or  two  in  large  vessels,  being 
so  shaped  as  to  engage  the  rudder  stop  at  hard-over.  This  post  is 
connected  to  the  main  structure  on  a  deep  transom  plate  clipped 
to  its  fore  side,  and  in  vessels  of  over  about  300  feet  in  length  the 
forward  or  body  post  must  also  be  carried  up  and  secured  in  a 
similar  manner.  The  body  post  is  swelled  around  the  stern  tube, 
having  a  sectional  area  through  the  eye  equal  to  the  frame  and 
meeting  the  post  above  and  below  in  a  fair  curve  ;  the  spur  or  keel 
part  of  frame  must  not  be  too  long  to  facilitate  handling,  the 
general  rule  being  about  2  J  frame  spaces  before  the  body  post, 
where  it  incorporates  with,  or  scarphs  into,  the  keel  as  already 
described. 

In  steamers  over  350  feet  length  where  these  frames  are  of 
considerable  weight,  the  riveting  connecting  body  post  to  hood  ends 
of  shell  plating  should  be  treble  below  boss  and  of  increased 
diameter  and  an  addition  made  to  the  plating  thickness.  As  in 
the  keels,  these  holes  must  be  carefully  drilled  and  where  scarphs 
are  introduced  as  in  the  case  of  frames  of  two  or  more  pieces  the 
riveted  connection  should  be  developed  to  equal  the  bar.  It  is 
common  to  make  the  contour  of  body  post  curvilinear,  thus  effect- 
ing an  appreciable  saving  in  weight  over  the  straight  line,  besides 
giving  a  more  graceful  form. 

In  small  steamers  the  after  or  rudder  post  may  be  dispensed 
with,  a  spur  being  carried  aft  from  body  post  to  support  heel  pintle. 


Rudders 


279 


For  single  screw  steamers  classed  to  Lloyds  the  weight  of  stern 
frame  may  be  very  closely  approximated  by  taking  the  first 
numeral  to  upper  deck  and  multiplying  it  by  240  for  vessels  over 
300  feet  in  length,  or  by  156  for  those  under  this  dimension,  as  first 
number  x  240  =  weight  in  pounds. 


RUDDERS. 

Some  of  the  more  common  forms  of  rudders  are  shown  in  Figs. 
138  to  143.     The  stresses  to  which    they  are  subjected  and 
method   of  determining  the    diameter    of 
stock   has   already    been    fully    described. 
The  single   plate  rudder,  Fig.    138,  is  the 
type  most  commonly  adopted  in  merchant 
steamers,  and  is  usually  built  in  three  parts, 
viz.  :  the  frame,  norman  head  and  plate. 
The  frame  may  be  either  cast  or  forged,  bolted  coupl, 
having  arms  or  stays  projecting  from  the 
stock  on  alternate  sides  of  centre  line  spaced 
opposite  each  of  the  gudgeons,  which  are 
from  4'  to  5'  6"  apart. 

The  norman  head  or  stock  should  be 
forged  in  iron  or  steel  with  a  coupling  palm 
at  lower  end  to  connect  with  a  similar 
palm  on  head  of  frame.  Allowance  should 
be  made  on  this  forging  for  machining  a 
key  to  lock  the  norman  head  to  the  frame, 
and  in  addition  turned  coupling  bolts  are 
fitted  with  nuts  on  under  side,  threads 
turned  off  to  a  thimble  point  and  split  pins 
fitted.  These  bolts  are  from  one  to  three 
inches  in  diameter  in  practice.  Their  size, 
however,  is  not  important,  as  the  shearing 
stresses  are  all  taken  on  the  key.  The 
stock  need  only  be  turned  in  wake  of  the 
rudder  quadrant  where  it  is  sometimes 
increased  in  diameter  to  compensate  for 
cutting  the  key  way. 

The  single  plate  forming  the  rudder  blade  is  fitted  between,  and 
riveted  to,  the  supporting  arms,  besides  engaging  a  groove  cut 
down  the  back  of  rudder  stock.  Its  thickness  ranges  from  about 
|"  in  small  steamers  to  1]  inches  in  liners. 

Braces  are  formed  at  the  ends  of  supporting  arms  which  are 
turned  out  to  take  fitted  pintles.  One  (two  in  large  rudders)  of 
these  braces  must  be  shaped  to  act  as  a  stopper  when  the  rud- 
der is  put   hard-over.     The   pintles   should   preferably   be   fitted 


Fio.  138. 


280 


The   Naval   Constructor 


separately  and.  of  the  cone  type  shown  in  the  detail.  It  is  bad 
practice  to  forge  pintles  on  the  frame,  as  besides  the  difficulty  of 
turning  them  in  a  lathe  they  have  the  disadvantage  of  not  being 
readily  renewable.  The  best  manner  of  bushing  the  pintles  is  a 
matter  of  opinion,  the  simplest  and  probably  the  one  most  favored 
being  to  make  the  bushes  of  hard  steel  with  a  flange  to  take  the 
tap  screws  securing  them  around  the  eye  of  the  braces.  The 
weight  of  the  rudder  in  small  vessels  is  taken  on  a  hard  steel  disc 
placed  in  the  heel  step  bearing  with  a  hole  through  the  heel  step 


BOLTED  COUPLING 


RIVETED  JOINT 


< 

< 

Z 

o 

I- 
o 

LU 
CO 


RIVETED  JOINT 


Fig.  139. 


Fig.  140. 


for  backing  it  out.  In  large  steamers,  however,  where  the  weight 
of  rudder  is  many  tons,  the  weight  should  always  be  taken  by  a 
carrier  seated  inside  the  counter.  Various  types  of  these  are 
shown  by  engravings  144  to  146.  Provision  must  be  made  on  the 
back  of  rudder  well  clear  of  wrater  line  to  fit  a  Jew's  harp  shackle 
for  securing  the  emergency  chains,  which  are  from  thence  carried 
up  the  counter,  being  stopped  with  ratline  stuff  to  tapped  eyes 
spaced  about  thirty  inches  apart. 

Next  in  favor  to  the  single  plate  is  the  cast  steel  rudder,  Fig.  139, 
although  where  only  one  is  being  made  its  cost  is  against  it.  For 
the  largest  sizes  its  difficulty  of  successful  manufacture  is  also  to 


Rudders 


281 


its  disadvantage,  although  this  is  got  over  by  casting  it  in  two  or 
more  pieces,  sec  Fig.  140,  keying  these  together  and  riveting  them 
through  coupling  flanges.  When  rudders  are  designed  to  be  cast 
in  one  piece,  the  ribs  which  are  cast  on  the  blade  to  act  as  stays 
should  be  of  easy  section,  so  as  not  to  interfere  more  than  neces- 
sary with  the  e< infraction  of  the  casting  in  cooling. 

The  oldest  method  of  making  the  rudder  for  steel  ships  is  the 
built  type,  Fig.  142,  which  consists  of  a  forged  frame  having  stock, 
stays,  and  back  piece  in  one,  with  two  side  plates  riveted  to  same 


A— 


--B 


FUr.  141. 


Fig.  142. 


Fig.  143. 


after  having  the  inside  filled  in  with  fir  coated  with  tar.  Its  great 
objection  is  the  cost  of  forging,  especially  for  large  rudders.  It  has 
gone  completely  out  of  favor  unless  for  yachts,  where  its  appear- 
ance commands  its  use,  and  in  light  craft  of  the  torpedo  boat  kind 
where  sufficient  stiffness  would  not  be  obtainable  in  a  single  plate 
without  going  into  a  thickness  which  would  make  the  weight  pro- 
hibitive. It  is  also  often  used  with  the  frame  cast  in  gun  metal 
and  the  side  plates  of  16  gauge  brass  sheet,  for  wood  speed 
launches,  vedettes,  pinnaces,  etc..  although  for  these  craft  a  cheaper 
and  lighter  rudder  may  be  obtained  by  casting  it  complete  in  gun 
metal  or  bronze. 


282 


The  Naval   Constructor 


RUDDER 


CARRIER 


i/f  \  \ 


Fig.  144. 


Rudders 


283 


OLTS 


Fig.  145. 


284 


The  Naval  Constructor 


WHITE    METAL. 


TSLVJI 


°f  "      -t-JV-'-y,,-^  4    •'" 

■A \ ^__s^-4  ->;  j"      "/a 

I  ii  ■  -       \  V 


4 
7} 


h  «T  f  CAST    IRON 

y  '"+  i      ~"        "  •'■".~^ll 


HARD  WOOD   FILLER 


BRASS   RING   9X34 


/ 


WOOD  FITTED  AFTER  RUDDER 
IS  HUNG  4  THICKNESS  MADE  ACCORCINGLV 


Fig.  146. 


Rudders 


285 


ELEVATION   OF 
COUPLING 


Fin.  147. 


286  The  Naval  Constructor 


Where  the  rudder  stock  enters  the  vessel,  watertightness  must 
be  ensured  by  fitting  a  trunk  having  a  stuffing  box  and  gland  at 
its  top.  This  latter,  however,  may  be  dispensed  with  where  a 
carrier  is  arranged  for,  this  being  an  additional  element  in  favor 
of  the  adoption  of  these  supports.  Before  fixing  on  the  counter 
dimension  of  the  rudder  trunk,  care  should  be  taken  that  ample 
clearness  is  given  to  ship  and  unship  the  rudder.  It  will  be  seen, 
therefore,  that  the  hole  through  the  counter  is  much  in  excess  of 
the  diameter  of  stock,  and  if  not  filled  in  would  be  unsightly,  be- 
sides allowing  a  considerable  volume  of  water  continually  at  play 
inside.  It  is  covered  in  with  a  tail  plate  fitted  in  halves  and  secured 
with  hexagon  head  taps  to  the  counter  plating,  so  as  to  be  easily 
removable  to  permit  of  unshipping  the  rudder. 

Good  proportions  for  such  details  as  pintles,  gudgeons,  braces, 
couplings,  etc.,  to  meet  most  requirements  are  shown  in  Fig.  147. 

PROPELLER   STRUTS. 

These  brackets  for  supporting  the  outer  end  of  tail  shaft  are  gen- 
erally of  pear-shaped  section  as  being  the  form  of  least  resistance. 
It  is  usual  to  cast  them  in  steel,  although  they  are  also  sometimes 
built  up. 

In  selecting  a  suitable  area  of  arm  shipbuilders  are  guided  mostly 
by  experience,  hence  the  divergent  results  seen  in  practice.  The 
author  has  therefore  devised  the  formula  given  on  p.  109,  in  which 
he  has  attempted  to  secure  a  uniform  relationship  between  the  size 
of  these  struts  and  the  power  transmitted  through  them. 

Where  possible  the  centre  of  the  propeller  bracket  should  be 
placed  on  a  frame  to  obtain  the  maximum  of  stiffness,  and  the 
palms  of  upper  and  lower  arms  may  be  cast  on  or  connected  with 
angle  clips.  A  web  spur  is  sometimes  cast  or  worked  on  keel 
length  of  stern  post  to  take  the  palm  of  lower  arm  instead  of  flang- 
ing the  latter  and  riveting  it  through  the  keel  to  it,  securing  inde- 
pendent connection  for  each  strut. 

In  wake  of  the  upper  palm  additional  stiffening  must  be  worked 
by  fitting  a  short  local  doubling  on  shell  and  a  stringer  inside.  The 
number  and  diameter  of  palm  fastenings  should  be  developed  ac- 
cording to  the  sectional  area  of  the  arm,  these  being  in  most  cases 
overdone. 

The  sectional  area  of  arms  must  not  be  tapered  towards  the 
boss,  as,  although  theoretically  considered  as  a  cantilever,  this  would 
be  rational,  it  must  not  be  lost  sight  of  that  the  greatest  stresses 
are  borne  by  the  ends  of  the  arms  adjoining  the  boss,  and  are,  be- 
sides, alternating  ones  inducing  fatigue. 

The  engineer  will  determine  the  length  of  boss  barrel  suitable 
for  bearing  and  also  the  finished  diameter  of  the  hole,  but  ample 


Casting  at  Stern   Tube 


281 


allowance  should  be  made  for  boring  out  to  this  dimension  and 
also  adjusting  to  centre  line  of  shaft ;  this  is  most  important  when 
dealing  with  cast  steel,  as  it  provides  the  opportunity  to  detect 
hidden  blow  holes.  A  mass  of  metal  should  be  avoided  where  the 
arm  swells  to  meet  the  boss  either  by  reducing  the  fillet  to  a  mini- 
mum or  coring  out  the  metal  inside  the  boss,  as  otherwise  internal 
stresses  will  be  set  up  in  cooling  or  dangerous  blow  holes  developed. 
In  high  speed  vessels  it  is  important  to  make  the  pattern 
"wind  "  conforming  to  the  run  of  the  water  line,  thus  obviating 
the  arms  being  dragged  across  the  stream  lines  and  creating  eddies. 
It  is  surprising  the  amount  of  power  absorbed  by  this  resistance 
when  brackets  are  badly  set  or  not  set  at  all. 

SPECTACLE   FRAMES. 

Spectacle  frames  have  nearly  superseded  the  open  A  brackets 
for  large  merchant  vessels.  They  are  enveloped  in  the  hull  of  the 
ship,  the  plating  being  webbed  out  and  bossed  around  the  shaft  for 
this  purpose,  as  fully  explained  in  the  chapter  on  Design,  which  see. 

Where  the  plating  ends  on  the  arms  of  these  frames  a  good 
riveted  connection  must  be  made,  usually  double  and  increased  to 
treble  tap  rivets  around  the  boss.  Local  strengthening  must  also 
be  fitted  in  wake  of  spectacle  frames  by  increasing  the  deep  floors 
in  thickness  and  doubling  the  ship's  frames  in  their  vicinity. 


CASTING   AT    STERN   TUBE. 

The  outboard  end  of  stern  tube  in  vessels  fitted  with  A  brackets  is 
supported  by  and  connected  to  a  steel  casting  or  forging.  Its  func- 
tion is  similar  to  the  boss  on  body  post  of  a  single  screw  steamer. 

STEEL  CASTING 

_  rsoccrn  SHELL   PLATING 

— ~z 


ZINC  RING 


HORIZONTAL  SECTION. 
Fig.  148. 


288 


The  Naval  Constructor 


Iu  large  steamers  it  is  usual  to  extend  this  casting  over  two 
frames  in  length  to  give  additional  support,  as  shown  in  Fig.  148, 
but  in  small  vessels  the  tube  end  support  need  only  be  from  2  to 
4  inches  thick,  and  shaped  like  Fig.  149.  Usually  a  watertight 
bulkhead  is  fitted  at  the  forward  and  after  ends  of  the  stern-tube, 
the  former  one  being  bossed  and  spectacled  at  the  wings  in  the 
manner  depicted  in  the  detail  given. 

The  inboard  palm  of  the  tube  end  forging  is  securely  riveted  to 


Fig.  149. 


wing  plate  of  bulkhead,  which  must  be  increased  in  thickness  for 
the  heavier  riveting  necessarily  employed  for  this  purpose. 


FRAMING. 

In  ships  having  ordinary  floors  the  frames  are  invariably  run  in 
one  piece  from  centre  line  to  gunwale,  and  where  channel  bars  or 
bulb  angles  are  employed  with  this  construction,  the  floor  plates 
may  be  reduced  in  consideration  of  the  excess  strength  given  in 
their  wake.  Vessels  having  a  double  bottom  on  the  cellular 
system  need  only  have  angle  frames  on  the  deep  floors  with  flanges 
sufficient  to  take  the  size  of  riveting  required.  Forward  in  the 
flat  of  bottom  in  full  vessels  these  should  be  doubled  inside  tank 
and  in  addition  local  fore  and  aft  stiffening  fitted  to  reenforce 
against  "  pounding. "'  Where  vessels  are  classed,  as  they  mostly 
are,  the  scantlings  of  the  frames  are  obtained  from  the  rules  of  the 
classification  bureau.  The  angle  bars  of  which  they  are  made  is 
always  one  with  unequal  legs,  the  larger  flange  standing  vertically 
to  the  shell  plating  to  obtain  the  greatest  section  modulus  in  the 
direction  of  the  pressure. 


Framinj 


289 


Where  frames  are  cut  at  margin  plates 
of  inner  bottoms  or  at  water  tight  flats, 
efficient  bracket  plates  of  such  dimen- 
sions as  will  permit  of  riveting  to  develop 
the  strength  of  frame  bars  should  be  fitted. 
See  Fig.  153  and  159.  In  wake  of  flats 
where  bracket  knees  are  objected  to  on 
account  of  the  broken  stowage  created,  or 
their  interference  with  cabin  arrai.- 
ments,  the  framing  may  be  continuous 
and  smithed  angle  collars  or  pressed  plate 
chocks  fitted  around  them  to  ensure  water 
tightness  as  in  Fig.  150.  For  simplicity 
in  forming  collars,  frame  and  reverse  bar 
or  channel  section,  the  reverse  bar,  or 
flange,  may  be  cut  off  and  the  frame  bar 
doubled  for  a  short  distance  above  and 
below  the  flat  as  compensation  as  in  Fig. 
151. 

Where  main  frames  are  stopped  at 
weather  deck  when  the  bridge  house  or 
superstructure  requires  a  bar  of  smaller 
section,  the  connection  between  weather 
deck  stringer  and  frame  may  be  com- 
pleted with  a  spirketting  plate  in  lieu  of 


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Fig. 150. 


.  151. 


knee 

latter 

would  encroach  on  the  berth- 
ing space,  as  shown  at  Figs. 
152  and  153. 

The  inboard  member  of  a 
ship's  framing,  called  the  re- 
verse bar,  whose  functions 
are  to  provide  a  flange  where- 
on to  fasten  the  ceiling,  or 
lining,  and  to  give  the  neces- 
sary section  modulus  by  ad- 
ding area  at  a  point  subjected 
to  corrosion  and  rough  treat- 
ment,  is  commonly  made  of 
angle  section  or  by  the  em- 
ployment of  channel  bar  for 
the  framing.  In  steamers, 
however,  under  about  100  feet 
it  will    be  found  economical 


290 


The   Naval   Constructor 


besides  being  good  construction  to  omit  the  reverse  bar  altogether 
and  increase  the  sided  flange  of  frame  angle  to  give  an  equivalent 


W.T.DK 


Fig.  152. 


Fig. 153. 


REVERSE   FRAME 


Fig.  154. 


I.      A   saving  in   material,  riveting  and  bending  will    thus  be 

effected.  In  light  vessels  where  weight  must  be  cut  down  with- 
out encroaching  on  the  strength,  the  maximum 
section  modulus  may  be  obtained  for  a  given  depth 
of  web  by  employing  two  bars  of  such  dimension 
of  leg  as  will  just  give  the  requisite  size  of  lap  to 
take  the  proper  riveting,  as  in  Fig.  154. 

The  practice  in  vogue  for  many  years  of  plac- 
ing the  frame  and  reverse  bars  back  to  back  has 
given  place  to  that  of  fitting  them  bosom  to 
bosom  where  deep  framing  is  adopted,  as  by  this 

method  the  beam  knees  can  be  fitted  without  linering  in  wake  of 

reverse  frames. 

FLOORS. 

The  deep  plates  riveted  to  the  bottom  framing  of  ships  and  known 
as  the  floors,  are  placed  there  to  resist  the  transverse  stresses  to 
which  the  bottom  plating  is  subjected,  due  to  the  great  water  pres- 
sure externally  applied,  and  the  inside  forces  created  by  the 
weight  of  the  structure  and  cargo. 

Ordinarily  in  ships  without  an  inner  bottom  these  are  of  a  size 
based  upon  the  breadth  and  depth  of  the  vessel  and  carried  in  a 
fair  line  up  the  bilge  to  a  height  equal  to  twice  the  centre  line  di- 
mension as  in  Fig.  155.  It  will  be  seen  that  this  contour  at  the 
bijge  necessitates  furnacmg  the  tail  ends  to  bend  them  to  the  re- 
quired curve,  a  costly  and  therefore  an  objectionable  feature.  For 
this  reason  ordinary  floors  should  be  increased  in  their  sided  areas 
and  carried  straight  across,  striking  the  bilge  at  a  point  somewhat 
lower  down  than  with  the  curved  floor.  This  method  permits  of 
the  floor  being  flanged  across  top  in  lieu  of  fitting  a  reverse  bar, 


Fl 


oors 


291 


although  some  of  the  classification  bureau  penalize  flanging  plates 
to  the  extent  of  adding  one-twentieth  to  their  thickness  :  this  need 
n<>t.  however,  be  made  unless  where  specifically  required  and  for 
that  reason  cheaper,  lighter,  and  equally  efficient  construction 
will  be  obtained. 

In  small  freight  steamers  and  barges  a  strong  and  inexpensive 
floor  is  obtained  by  using  structural  channel  section  thus  elimi- 
nating the  riveting  to  frame  and  reverse  bar  altogether. 

Floors  in  inner  bottoms  are  almost  entirely  fitted  as  deep  solid 
plates  in  one  piece  from  centre  vertical  keel  to  margin  plate,  light- 
ened with  large  manholes  to  cut  out  superfluous  material  and  pro- 
vide access  to  the  various  compartments  into  which  the  bottom  is 
sub-divided  by  the  doors  and  intercostal  girders.  Deep  floors 
should  be  lapped  to  the  bottom  frames  just  sufficient  to  take  the 
riveting.     In  wake  of  watertight  bulkheads  or  at  ends  of  ballast 


T 


Fig.  loo. 


Fig.  15G. 


tanks  where  the  floors  are  watertight,  no  holes  whatever  must  be 
cut  in  them.  The  margin  plate  of  inner  bottom  being  continuous, 
is  connected  to  the  main  frame  by  a  large  bracket  plate  or  tail 
piece,  and  by  double  angles  having  a  specified  number  of  rivets 
and  a  gusset  plate  at  top,  or  in  the  largest  vessels  a  continuous 
stringer.  The  connection  to  the  siding  flange  of  main  frame 
is  by  lap  of  sufficient  width  to  take  the  riveting.  See  Figs.  157 
and  168. 

Ar  the  ends  of  the  vessel  where  the  waterline  at  top  of  floor 
would  necessarily  be  comparatively  narrow,  increased  depth  must 
be  given  to  provide  compensatory  area  and  also  ensure  sufficient 
width  to  clip  the  centre  keelson  to  floors.  In  the  fore  peak  this 
additional  depth  is  required  to  resist  buckling  and  panting,  and  gen- 
erally to  give  local  stiffening  at  a  part  subjected  to  unusual 
stresses.  It  is  also  necessary  to  increase  the  floors  considerably  in 
depth  in  after-peak,  owing  to  the  severe  stresses  encountered  when 
the  propeller  "  races  "  and  the  stern  is  in  air. 


292 


The   Naval   Constructor 


INNER  BOTTOM. 


Double  bottoms  are  fitted  in  vessels  to  enable  them  to  safely 
make  voyages  "  in  ballast "  without  incurring  heavy  expenses  by 
loading  and  discharging  dry  ballast.  For  this  purpose  the  floors 
are  plated  over,  forming  an  inner  bottom  enclosing  with  the  ship's 
plating  a  pontoon  in  which  to  carry  sea  water  as  ballast,  an  expe- 
ditious, inexpensive  and  clean  method  of  doing  so.  Two  or  three 
methods  of  fitting  water  bottoms  are  met  with  in  practice,  but  as 
these  have  given  way  to  the  cellular  system,  it  is  unnecessary  to 
describe  them.  This  method  consists  in  the  subdivision  of  the 
space  formed  by  the  pontoon  referred  to,  into  a  great  number  of 
small  compartments  or  cells  bounded  by  the  floors  in  a  fore  and 
aft  direction  and  transversely  by  intercostal  girder  plates,  making 
these  cells  approximately  two  feet  by  four  feet,  respectively,  by 

the  depth  of  water  bot- 
tom. The  water  pas- 
ses freely  between  these 
cells  as  the  floors  and 
intercostal s  are  pierced 
with  access  holes  unless 
where  mentioned  here- 
after.      The    cells    are 

1       j  'fifi"    /""""N       /  ///      arranged     in     separate 

i J\W      \       )     /  Jy         groups  or  compartments 

enclosed  by  the  centre 
vertical  girder,  water- 
tight floors  and  the 
margin  plate,  this  larger 
Fig.  157.  subdivision  being  neces- 

sary for  trimming  and  filling  purposes,  as  otherwise  a  large 
surface  of  free  water  would  be  highly  dangerous  in  certain 
conditions. 

As  mentioned,  the  centre  vertical  plate  is  continuous  fore  and 
aft,  fitted  usually  watertight  and  connected  top  and  bottom  to  in- 
ner plating  and  plate  keel  with  suitable  angle  bars.  No  holes  what- 
ever should  therefore  be  cut  through  vertical  keel  plate,  and  al- 
though it  is  not  necessary  to  caulk  it  in  way  of  ballast  tanks,  the 
riveting  should  be  of  watertight  pitch.  Of  course  where  fresh 
water  is  carried  this  longitudinal  girder  must  be  properly  caulked. 
At  the  ends  of  the  vessel  where  fore  and  aft  subdivision  is  unnec- 
essary the  centre  plate  may  have  access  manholes  as  in  the 
floors. 

The  butt  connections  are  preferably  formed  with  double  butt 
straps,  each  of  about  two-thirds  the  thickness  of  plate.     Through 


Inner   Bottom 


293 


Fig.  15S. 


butts  should  not  be  used  here,   as  besides  interfering  with  the 

passage  of  the  fore  and  aft   angles  they  only  give   single  shear 
value   to  the  riveted   con- 
nection. 

The  outboard  side  of  the 
inner  bottom,  or  margin 
plate,  is  fitted  to  shell  by 
means  of  a  continuous  an- 
gle bar,  the  main  frames  of 
the  ship  being  cut  for  that 
purpose.  At  the  top  this 
plate  is  flanged  in  board  to 
take  the  inner  bottom  plat- 
ing as  shown  in  Fig.  157.  The  butts  of  margin  plate  are  covered 
with  single  strap  fitted  on  the  inside  of  tank. 

This  plate  may  also  be  fitted  with  advantage  as  shown  in  Fig. 
158  devised  by  the  author,  which  consists  in  flanging  the  plate  out- 
board,   a   shape   that  the  plate  will  take  more  naturally  where 

there  is  curvature  in  a  fore 
and  aft  direction.  This  out- 
board flange  will  also  permit 
of  machine  riveting  and  con- 
necting to  the  reverse  flange  or 
bar  on  the  floor  bracket,  thus 
forming  a  continuous  stringer  ; 
or,  angle  section  may  be  sub- 
stituted for  the  flange  where 
facilities  for  bending  are  not 
obtainable. 

Another  method  of  fitting 
the  margin  is  illustrated  by 
Fig.  159,  where  the  top  plat- 
ing is  carried  right  out  to  the 
shell  and  flanged  upwards  to 
take  staggered  riveting.  Flan- 
ging is  preferable  to  fitting  an  angle  bar,  as  in  the  latter  case 
difficulty  would  be  experienced  in  putting  in  the  rivets  on  the 
horizontal  flange  of  the  bar.  It  is,  however,  a  cheap  method  of 
construction,  its  principal  objection  beiug  the  broken  stowage 
caused  by  the  brackets  connecting  frame  to  inner  bottom. 

The  inner  bottom  plating  will  be  of  such  thickness  as  the 
classification  societies  stipulate  where  the  vessel  is  classed,  when 
it  will  be  found  that  increased  scantling  is  required  under  engines 
and  boilers,  and  of  course  the  centre  strake  and  margin  plate  will 
also  be  thicker  than  the  rest  of  the  plating,  owing  t<»  the  former 
being  the  rider  plate  member  of  the  girder  formed  by  the  centre 


Fig.  159. 


294 


The   Naval   Constructor 


vertical  keel  and  keel  plate,  and  the  latter  being  an  important 
factor  in  the  longitudinal  strength  of  the  ship.  For  this  reason 
when  arranging  the  access  manholes,  these  must  always  be  kept 
clear  of  the  centre  strake.  A  good  shift  of  butts  must  be 
arranged  for  the  plating,  and  these  shifted  clear  of  the  butts  of 
shell,  margin  plate  and  longitudinals. 

Where  the  strakes  of  inner  bottom  plating  are  arranged  "in  and 
out,"  the  packing  liners  to  outside  strakes  should  be  fitted  short, 
the  unfilled  spaces  acting  as  air  holes. 

The  practice  of  fitting  wood  ceiling  on  tank  tops  is  giving  way 
to  coating  the  plating,  with  tar  or  bitumastic  cement,  as  this  pre- 
vents the  deterioration  that  goes  on  under  the  wood,  besides  adding 
to  the  stowage  capacity.     Where, however,  wood  ceiling  is  required, 

it  must  be  laid  on  fore  and 
aft  bearers  and  screwed  to 
same  and  not  fastened  through 
tank  top.  For  this  reason, 
ie.,  guarding  against  leakage 
the  heels  of  the  hold  pillars 
are  riveted  to  vertical  flange 
of  tee  or  angle  lugs  which 
are  first  riveted  through  in- 
ner bottom. 

In  arranging  the  manholes 
care  should  be  exercised  that 
they  are  located  in  accessible 
parts  of  holds  and  clear  of 
cargo  hatches.  In  holds  of 
ordinary  length  one  each 
side  at  each  end  about  quar- 
ter the  beam  outboard  will 
be  sufficient,  and  in  long  holds 
an  additional  one  about  the 
middle  of  the  length.  In  no 
case  as  previously  pointed 
out  should  they  go  through 
the  centre  strake.  The  best 
location  aft  will  of  course  be 
in  tunnel  alleyways,  and  in 
machinery  spaces  they  should 
be  fixed  by  the  engineers. 
This  arrangement  will  contribute  to  the  best  circulation  of  air 
when  the  covers  are  taken  off  for  ventilating  purposes.  Ample 
room  must  be  allowed  for  rim  of  manhole  to  clear  landings, 
butts,  longitudinal  clips,  etc. 
The  shell  plating  forming  the  bottom  of  tanks  may  be  reduced 


Fig.  160. 


Beams  295 

in  thickness  in  consideration  of  the  extra  strength  added  by  this 
construction,  and  the  broad  liners  fitted  to  outside  strakes  in  wake 
of  watertight  bulkheads  may  be  replaced  by  narrow  liners  at 
watertight  floors  in  tanks. 

To  drain  the  various  compartments  of  the  double  bottom  when 
the  ship  is  in  dry  dock,  screw  plugs  of  composition  are  fitted  in 
the  garboard  strake  and  a  compensating  plate  riveted  around  the 
hole.  A  detail  of  such  a  fitting  is  shown  by  Fig.  160.  It  is  usual 
to  fit  similar  plugs  in  the  trimming  tanks  at  fore  and  after  peaks. 


BEAMS. 

Beams  are  fitted  at  various  levels,  or  decks,  to  tie  the  ship  to- 
gether and  afford  supports  whereon  to  lay  the  decks  to  take  car- 
_  "S.  The  strength  of  these  will  depend  therefore  on  the  load  as 
well  as  the  span  or  breadth  of  beam,  as  it  will  be  seen  that  a 
weather  deck  beam  need  not  be  as  strong  as  the  one  under  it,  and 
so  on — each  successive  tier  taking  the  accumulated  load  super- 
imposed. 

It  is  common  practice  to  give  all  decks  a  round-up  or  camber, 
an  expensive  practice  that  is  unnecessary  unless  on  the  weather 
deck,  and  only  necessary  there  in  a  modified  sense  to  obtain  the 
statutory  freeboard  or  to  conform  to  classification  requirements. 
It  is  a  fallacy  to  imagine  that  strength  is  gained  by  cambering  the 
beams  thus  supposedly  constructing  an  arch,  as  you  cannot  have 
a  compressed  beam  without  abutments,  which  the  sides  of  the  ship 
are  not.  To  meet  the  requirements  mentioned  above,  the  weather 
deck  should  have  the  standard  camber  of  one-quarter  iuch  to  the 
foot  of  length,  thus  a 
beam  40  feet  long  will 
have  a  round-up  at  cen- 
tre line  of  ten  inches. 
This  curve  may  be  set 
off  very  quickly  with 
the  aid  of  a  common 
slide  rule  by  setting  the 
courser  to  the  required 
round-up  on  the  first  or 

top  scale  and  to  the  half  beam  on  the  third  scale,  when  the 
camber  at  any  desired  distance  in  board  of  ship's  side  may  be 
found  by  moving  the  courser  to  the  dimension  required  and  read- 
ing off  on  top  scale.  The  reading  subtracted  from  the  total 
camber  will  give  the  required  round-up.  This  may  also  be  figured 
as  shown  in  Fig.  161.     The  beams  are  connected   to  the  "main 


296 


The  Naval   Constructor 


Figs.  162-167 


B 


earns 


297 


THICKNESS    OF    BRACKETS    DEPENDS    ON 
WEIGHT    OF    BEAM    PER    FOOT. 

See  Figs.  162  164.) 


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298 


The   Naval   Constructor 


TO    FIT    CARNEGIE'S    1897     PATTERNS. 


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III 


Beams  299 


frames  by  welded  knees  or  bracket-plates,  the  latter  being  much 
the  cheaper  and,  where  appearance  is  not  important,  the  better 
method.  The  depth  of  these  knees  is  commonly  21  times  the 
depth  of  beam  if  of  channel  or  bulb  tee  section,  and  three  times 
the  depth  if  angle  bar  be  used.  The  thickness  should  be  the  same 
as  the  beam  unless  where  welded  knees  are  fitted,  when  it  is  good 
practice  to  increase  the  plate  one-sixteenth  to  allow  for  loss  in 
smithing.  When  dealing  with  beams  conforming  to  Lloyd's  Rules, 
it  should  be  noted  that  the  bracket  knees  are  regulated  in  depth 
and  thickness  by  the  size  of  the  bulb  plate  required  by  the  table, 
irrespective  of  the  dimensions  of  the  substituted  equivalent  sec- 
tion of  channel,  bulb  angle,  or  bulb  tee.  For  example,  if  the  rules 
require  a  built  beam  of  bulb  plate  and  angles,  the  former  being 
1()|"  X  ifr",  and  it  was  decided  to  fit  the  equivalent  channel  bar 
of  11"  X~3V"  x  iy\  then  the  bracket  knee  would  be  26|"  x  ft". 

Standard  beam  knees  as  used  in  Navy  practice  are  shown  by 
Figs.  162  to  167.  In  arranging  the  riveting  in  plate  knees,  the  re- 
quired number  is  usually  specified  for  classed  vessels,  and  as  these 
are  invariably  staggered,  it  is  well  to  locate  the  first  rivet  hole  as 
far  outboard  on  the  beam,  and  down  on  the  frame,  as  practicable. 
Those  in  the  corner  may  be  treated  as  common  to  both  arms  in 
counting  the  number  required. 

Where  unsheathed  steel  decks  less  than  ^V'  thick  are  fitted,  beams 
must  be  fitted  on  every  frame,  with  stronger  beams  at  ends  of  cargo 
hatchways.  Where  the  thickness  is  ^  or  over,  the  beams  may  be 
fitted  on  alternate  frames  with  half  beams  on  every  frame  abreast 
of  hatches.  When  this  spacing  is  adopted,  most  societies  require 
closer  spacing  of  rivets  through  deck  plating,  viz.,  5  diameters 
apart  as  against  7  to  8  diameters  with  the  closer  spaced  beams,  so 
that  it  is  doubtful  economy  at  a  sacrifice  of  efficiency  to  space 
them  on  alternate  frames. 

In  the  machinery  spaces  of  steamers  it  is  necessary  to  fit  beams 
of  extra  strength  wherever  these  can  be  worked  without  interfer- 
ing with  the  arrangement  of  engines  and  boilers.  These  through 
beams  compensate  for  the  loss  in  transverse  strength  through  the 
severance  of  the  regular  deck  beams  at  the  large  machinery  open- 
ings, and  serve  to  tie  the  ship  together  and  prevent  panting  of  the 
sides  at  a  part  where  a  considerable  weight  is  permanently 
carried.  In  large  steamers  the  machinery  arrangement  often 
permits  of  two  adjoining  through  beams  being  tied  together  by 
cover  plates,  thus  forming  an  exceptionally  strong  beam  of  box  sec- 
tion. Where  Btrong  beams  cannot  be  fitted  in  one  piece,  owing  to 
interference  with  the  shipping  of  parts,  they  should  be  efficiently 
bracketed  to  the  casing  coamings,  care  being  taken  that  the  con- 
nection develops  the  strength  of  beam.  When  practicable  the  pil- 
lars in  machinery  spaces  should  be  fitted  on  these  through  beams. 


300 


The   Naval   Constructor 


ANGLE  BEAM  COLLAR 


-  — 6V2 


The  term  half  beam  is  applied  to  those  deck  beams  which  are 
severed  in  wake  of  hatch  openings.  Their  inboard  ends  abut  on 
the  hatch  side  coaming  plates,  which  are  in  consequence  made 
thicker  than  the  end  ones,  and  the  connection  is  commonly  by  a 
single  angle  clip  (taking  a  specified  number  of  rivets)  if  a  continu- 
ous fore  and  aft  angle  is  fitted  at  bottom  of  plate  to  support  the 
beam  ends,  or  the  coaming  plate  is  flanged  under  the  beams  for  a 
like  purpose.  It  will  be  thus  seen  that  this  rest  will  take  a  great 
deal  of  the  shear  off  the  rivet  connection,  besides  adding  to  the 
strength  of  the  girder  formed  by  the  coaming. 
In  wake  of  small  deck  openings  the  inboard  beam  end  may  be 

supported  by  acarling,  or  fore 
and  after,  of  similar  section  to 
the  beam,  except  where  bulb 
tee  is  used  with  the  heel  of  the 
carling  abutting  on  beam  end 
and  connected  to  same  with, 
preferably,  double  clips  so  as 
to  get  double  shear  value  from 
the  rivets. 

Where  heavy  local  weights 
or  deck  machinery  are  secured, 
the  beams  in  wake  of  same 
should  be  increased  in  sec- 
tion, and  special  pillaring  or 
deck  girders  fitted.  It,  is  like- 
wise necessary  to  increase  the  strength  of  the  beams  at  the  ends 
of  hatchways  by  adding  to  their  sectional  area  —  but  not  to  their 
depth  if  avoidable. 

The  beams  supporting  bridge  or  shade  decks  fitted  over  houses 
and  extending  to  ship's  side  are  frequently  carried  thwartship  in 
one  bar,  the  casings  being  scored  out  and  watertight  collars  fitted, 
in  preference  to  cutting  the  beams  and  fitting  bracket  plates. 
These  collars  are  shown  by  Fig.  171,  and  may  be  smithed,  stamped, 
or  cast  in  steel  or  malleable  cast  iron. 


SPLIT  HERE 


Fig.  171. 


Hold   Pillars 


301 


HOLD    PILLARS. 

Support  is  given  the  beams  on  the  various  decks  by  stanchions. 
Various  sections  are  employed  for  this  purpose,  as  round  bar,  pipe, 
/  section  and  columns  built  of  channel  <>r  plate  and  angle  bar. 
F<>r  vessels  carrying  general  cargoes,  ibe  pipe  section,  being  circu- 
lar and  light,  is  probably  the  best.     The  I  section  makes  a  very 


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cheap  and  efficient  column,  as  forged  ends  are  done  away  with  ; 
and  in  vessels  requiring  large,  clear,  stowage  spaces  in  holds,  built 
columns  should  be  fitted  connected  to  strong  deck  girders.  A 
v.  iv  efficienl  type  of  built  column  is  shown  by  Fig.  172.  passed  by 
Lloyd's  Register  for  a  span  of  .'X)  feet. 


302 


The  Naval  Constructor 


DETAILS    OP   HEADS    AND    HEELS   FOR  PIPE 

STANCHIONS. 


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LlOtOS  REQUIRE  THESE  70   BE   FORGCD    AND   WELOED   INTO   PIPE 
WITH    A   SUITABLE   HAMMER  .Tri  EY    MAY    BE   DlE-'ORoED 
FuR  SHIPS  NUT    CLASSED   AT   LLOYDSiA  STEEL   C4STIN6 
WILL   6E   MORE   ECONOMICAL   AND  EQUALLY    EFflf ItHT,, 


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NOTE.  FOR  STANDARD  PIPE  ELEMENTS   SEE  TABLES 


Figs.  173  to  186. 


Hatches  303 

Where  pipe  pillars  are  adopted,  the  accompanying  diagram 
giving  types  of  solid  heads  and  feet  will  be  found  useful. 

It  will  be  obvious  that  the  hold  pillars  must  be  stronger  than 
those  in  the  lower  'tween  decks,  the  sizes  being  gradually  reduced 
as  we  approach  the  upper  works,  owing  to  the  reduction  in  the 
load  which  the  successive  tiers  of  pillars  support. 

As  pillars  are  intended  to  take  compressive  stresses  their  relative 
strengtli  with  a  uiven  section  is  entirely  in  the  end  connections, 
and  as  the  strongest  of  these  is  a  fixed  closely  fitted  fat  end,  this 
form  should  be  adopted  wherever  possible.  Where,  however,  it 
cannot  be  fitted,  as  on  tank  tops  and  with  beams  of  section  other 
than  channel  where  no  ridge  bars  are  worked,  care  should  be 
taken  to  fit  closely  the  heads  and  heels  on  their  supports,  so  that 
the  load  shall  be  taken  on  the  column  and  not  as  a  shearing  stress 
on  their  fastenings,  which  should  be  relieved  wherever  possible  of 
doins;  work. 

In  larger  vessels,  ridge  bars  of  channel  section  are  fitted  under 
the  beams  to  distribute  the  load  taken  by  the  pillars  over  all  the 
beams  and  also  to  prevent  the  beams  from  tripping.  In  wake  of 
hatchways  where  pillars  are  omitted  or  are  fewer  in  number,  inter- 
costal plates  are  fitted  between  the  beams  and  riveted  to  deck  as 
compensation,  thus  forming  a  deck  girder. 

When  hold  pillars  are  stepped  on  inner  bottom  plating,  a  short 
piece  of  tee  bar  must  first  be  riveted  to  tank  top  and  caulked,  and 
the  heel  of  pillar  afterwards  riveted  to  the  vertical  stem  of  tee  bar. 
A  similar  arrangement  is  adopted  on  expansion  trunk  tops  of  oil 
steamers  for  heels  of  gangway  stanchions. 

Where  grain  or  other  cargoes  liable  to  shift  are  carried  occasion- 
ally, the  hold  pillars  may  be  staggered,  the  heads  taking  alternate 
flanges  of  the  centre  line  ridge  bar,  thus  providing  an  intervening 
space  in  which  to  fit  the  shifting  boards. 

HATCHES. 

It  will  be  seen  that  a  serious  loss  in  transverse  strength  is  sus- 
tained by  cutting  the  beams  and  decks  to  form  hatchways,  and  it 
has  been  explained  under  the  caption  beams  how  this  loss  is  com- 
pensated for  in  the  deck  framing  and  by  increasing  the  sectional 
area  of  the  side  coaming  plates. 

Hatchways  should  be  no  larger  than  the  demands  of  the  par- 
ticular trade  call  for,  and  the  corners  of  these  openings,  at  least 
on  the  strength  deck,  should  be  round.  While  it  is  cheaper  to 
make  them  square,  it  will  be  found  false  economy.  In  addition  to 
making  them  round  on  the  strength  deck  the  corners  must  be  re- 
enforced  with  doubling  plates  extending  about  2  frame  spaces  each 
way  and  carried  18  inches  or  so  around  the  corners.     The  coam- 


304 


The   Naval   Constructor 


ing  angle  bar  must  be  welded  ;  or  a  much  better  method  is  to  run 
this  bar  to  within  nearly  four  feet  of  the  corners  around  which 

another  section  is  fitted  having 
a  much  broader  flange  on  deck  ; 
this  will  permit  of  staggering 
the  rivets  and  so  allow  more 
space  for  sufficient  riveting  at 
the  junction  of  this  bar  with 
the  deck  beam.  No  bosom  piece 
need  be  fitted  to  cover  the  butt 
of  the  corner  piece  with  the 
straight  length  of  coaming  an- 
gle, Fig.  187. 

End  coaming  plates  should 
have  "pitch"  in  preference  to 
camber,  as  they  are  more  easily 
made  and  allow  of  better  fitting 
the  wood   hatch   covers.      The 


Fig.  187. 


height  of  coamings  on  weather  deck  must  be  from  2  feet  to  2  feet 
6  inches,  and  on  other  decks  from  9  to  12  inches,  care  being 
taken  that  sufficient  height  is  given  to  permit  of  the  hatch  batten- 


J. 


STANDARD 
21/2---J     HATCH  CLEAT 


Jt.i._ 


DRILL  FOR  %  DlA. 
CSK.  RIVET 


Fig.  188. 

ing  cleats  being  fitted.  At  butts  of  coaming  plates  the  covering 
strap  should  be  fitted  on  the  outside  and  the  rivets  countersunk 
on  both  sides. 

A  typical  battening  cleat  is  shown  by  Fig.  188.  These  may  be 
either  die  forged  or  cast  in  steel  and  spaced  not  greater  than  2 
feet  apart  along  the  coaming  plate,  beginning  about  nine  or  ten 


Web   Frames 


305 


inches  from  the  corners  and  sufficiently  far  down  to  give  an  easy- 
fit  for  tarpaulin.  The  battening  bar  is  of  galvanized  flat  iron 
about  2 i  x  |",  and  the  butts  of  same  must  not  be  at  corners,  the 
bar  being  bent  round  these  to  allow  of  fitting  the  canvas  snugly. 
The  tarpaulin  is  then  secured  by  elm  or  oak  wedges. 

The  ledges  on  top  of  coamings  are  mostly  made  of  a  special 
rolled  section  as  shown,  although  where  this  is  not  obtainable  a 
zee  bar  will  answer  equally  well.  These  ledges 
should  be  mitred  at  the  corners  and  of  sufficient 
depth  to  house  the  hatch  covers.  In  addition  to 
the  support  afforded  these  by  the  ledge  bar,  fore 
and  afters  must  be  fitted,  as  well  as  bridle  beams, 
to  tie  the  hatchway,  in  number  and  scantling  as 
required  by  the  classification  societies.  The  fore 
and  afters  are  supported  by  rests  riveted  inside 
the  end  coamings  and  the  hatch  beams  by  socket 
slides  on  the  sides.  The  only  other  mountings  re- 
quired on  cargo  hatches  are  a  couple  of  lashing 
rings  on  each  side  fitted  about  four  feet  from  the 
ends  ;  these  may  be  riveted  on  coaming  plate  or 
deck  at  discretion. 

The  wood  covers  should  not  exceed  24  inches  in  width,  as  other- 
wise they  are  too  heavy,  and  are  usually  made  of  three  pine  deals, 
tie  bolted  with  three  §"  diam.  blind  bolts.  On  the  right  hand 
sides  of  top  a  lifting  bar  of  iron  through-fastened  with  two  clench 
bolts  is  fitted,  one  at  each  end,  and  the  wood  drilled  out  about  5 
inches  in  diameter  to  form  a  receptacle  for  the  hand.  These 
covers  must  have  properly  cut-iu  marks  to  facilitate  replacing 
them. 


WEB  FRAMES 


Web,  or,  as  they  are  sometimes  called,  belt,  frames  are  commonly 
formed  by  fitting  a  plate  from  15"  to  30"  deep  to  the  ordinary 
ship's  frame,  and  riveting  an  angle  bar  on  the  inner  edge  to  stif- 
fen and  add  to  the  resistance  of  the  web.  They  may  be  also  built 
with  double  channel  frames  with  a  covering  plate  on  face  —  an  ad- 
vantageous method  where  increased  room  or  stowage  capacity  is 
desired.  Still  another  method  is  to  fit  frames  and  reverse  bars  of 
similar  section  of  angles,  webbing  them  as  far  apart  as  possible 
consistent  with  the  requirements  of  the  riveted  overlap.  These 
various  methods  of  constructing  web  frames  have  all  the  same  ob- 
ject in  view,  viz.  :  to  give  the  equivalent  compensatory  transverse 
strength  lost  by  omitting  hold  beams  where  large  spaces  are  re- 
quired for  the  stowage  of  certain  freights  or  in  machinery  spaces 
where  hold  beams  cannot  be  fitted.  It  will  be  seen  that  these 
beams  really  perform  the  function  of  struts  tending  to  resist  the 


306  The   Naval   Constructor 


water  pressures  on  the  ship's  sides  and  the  hold  cargo  ;  and  for  this 
reason,  as  well  as  those  already  given,  should  have  no  camber 
which  it  is  conceivable  tends  to  weaken  them.  If  the  hold  beams 
then  be  left  out,  the  necessary  resistance  may  be  given  by  increas- 
ing the  section  modulus  of  the  side  framing,  and  this  is  obtained 
by  adding  webbed  frames  at  stated  intervals  along  the  sides,  and 
by  the  more  uniform  subdivision  in  a  vertical  direction  of  the 
areas  enclosed,  by  side  stringers  fitted  intercostally  between  webs 
having  a  covering  plate  at  their  intersection,  of  diamond  or  half- 
diamond  shape.  The  side  stringers  should  stand  squarely  to  the 
ship's  frame,  thereby  insuring  the  maximum  moment  of  resistance 
from  the  material  used,  as  well  as  avoiding  much  bevelling  of  angle 
bars. 

In  addition  to  the  foregoing,  web  frames  are  fitted  wherever 
local  losses  in  transverse  strength  take  place,  as  at  the  sides  of 
cargo  doors  and  similar  openings  and  over  abrupt  terminations  of 
transverse  strength,  such  as  take  place  where  a  watertight  bulk- 
head stops  short  of  the  strength  deck.  They  are  also  necessary 
where  exceptional  local  stresses  of  the  nature  indicated  are  applied. 

KEELSONS. 

The  value  of  keelsons  lies  in  their  contribution  to  the  lon- 
gitudinal strength  of  the  structure,  and,  where  they  are  fitted 
in  conjunction  with  intercostal  plates  having  a  shell  connec- 
tion, to  the  additional  assistance  given  to  the  hull  plating.  In 
general  practice  it  would  seem  that  too  much  prominence  is  given 
to  their  strength  as  individual  members  rather  than  treating  them 
as  component  members  of  the  main  structure,  or  ship  itself  viewed 
as  a  girder  ;  this  is  seen  in  the  deep  centre  line  keelsons  fitted  on 
top  of  ordinary  floors;  where  continuous  centre  vertical  plates  are 
also  fitted,  the  necessary  efficiency  and  strength  required  locally 
may  be  obtained  by  thickening  the  lower  parts  of  the  member,  as 
shown  in  Fig.  135,  and  at  the  same  time  increasing  the  moment  of 
inertia  of  the  ship's  section  as  a  whole  about  the  neutral  axis. 
Side  stringers  should  be  treated  similarly,  as  illustrated 
by  the  adjoining  sketch,  the  web  instead  of  one  flange 
of  the  channel  beihg  fitted  against  the  reverse  frame, 
permitting  of  a  better  connection  thereto,  at  the  same 
time  distributing  the  resistance  to  fluid  pressures  over 
a  greater  surface  and  adding  appreciably  to  the  stow- 
age capacity  of  the  vessel. 

Where  the  plates  forming  side  stringers  are  18  inches 

(or  over)  wide,  bracket  plates  must  be  fitted  underneath 

■  to  support  and  keep  them  standing  to  their  work,  except 

J    where  webs  are  8  feet  apart.    These  brackets  should  be 


> 


Fig.  190.    fitted  mia.way  between  the  web  frames. 


Bulkheads  307 

The  practice  of  piercing  watertight  bulkheads  with  keelsons  and 
stringers,  and  fitting  angle  collars  around  them  to  insure  water- 
tightness,  should  be  discouraged,  as  a  much  stronger  member  is  ob- 
tained by  cutting  the  keelson  or  stringer  and  connecting  same  by 
bracket  plates  to  the  bulkhead.  Tins  method,  besides,  gives  a 
more  reliably  watertight  connection. 

In  arranging  keelsons  or  bottom  longitudinals,  these  where  pos- 
sible should  be  incorporated  with  engine  foundation  girders,  or  if 
this  be  impracticable,  an  ethcient  scarph  should  be  made  by  con- 
tinuing them  past  one  another  for  about  three  frame  spaces  before 
terminating. 

In  ships  of  full  form  or  where  the  flat  of  floor  is  carried  well 
forward,  additional  intermediate  longitudinals  must  be  fitted 
locally,  about  half  the  depth  of  centre  girder  and  connected  to 
bottom  plating  to  re-enforce  the  shell  against  "pounding." 

Keelsons,  longitudinals,  or  side  stringers  should  never  terminate 
abruptly,  but  wherever  practicable  should  be  ended  on  and  brack- 
eted to  such  supports  as  bulkheads,  web  frames,  deep  floors,  etc. 
(are  should  also  be  taken  to  arrange  the  butts  of  these  members 
clear  of  shell  butts  as  well  as  "  shifted  "  with  one  another.  The 
rivets  in  the  strap  pieces  should  be  developed  to  equal  the  strength 
of  the  member,  and  double  shear  value  obtained  in  these  connec- 
tions wherever  possible. 

BULKHEADS. 

The  steel  divisional  partitions,  built  in  ships,  called  "bulkheads," 
were  primarily  fitted  to  isolate  the  living  and  machinery  spaces 
from  the  cargo  holds  proper,  but  were  soon  recognized  as  having  a 
more  important  mission  in  subdividing  the  ship  into  watertight 
compartments  besides  adding  considerably  to  transverse  strength. 
S  that  in  later  years  it  has  become  a  canon  in  ship  design  that  a 
vessel's  bulkheads  shall  be  in  number  and  arrangement  sufficient 
to  keep  the  ship  afloat  with  any  two  compartments  open  to  the 
sea.  Watertight  bulkheads  must  always  be  carried  to  the  deck 
above  the  load  waterline,  and  in  the  case  of  the  collision  or  fore- 
most one,  to  the  weather  deck,  as  the  forepeak  is  the  most  liable 
to  damage  and  flooding,  producing  a  great  alteration  in  trim. 
They  may  be  plated  either  vertically  or  horizontally,  and  efficiently 
stiffened  in  accordance  with  the  requirements  of  the  classification 
societies'  rules,  observing  in  arranging  stiffeners  that  these  are 
placed  on  the  reverse  to  the  caulking  side.  In  most  yards  the 
practice  is  to  fit  watertight  bulkheads  continuous  from  tank  top 
to  deck  level,  but  it  is  considered  better  construction  to  fit  the 
si     1  decks  continuous  and  the  bulkheads  intercostally. 

As  these  steel  partitions  are  connected  to  the  ship's  side  by  single 


308  The   Naval   Constructor 

or  double  angle  frames  with  closely  spaced  rivets  in  the  sided 
flange,  it  will  be  seen  that  this  line  of  perforations  around  the  shell 
is  a  source  of  weakness.  To  compensate  as  far  as  possible  for 
this,  it  is  necessary  to  fit  doubling  plates,  or  "liners,1'  where 
practicable,  i.e.,  in  wake  of  the  outside  strakes  of  shell  plating. 
These  liners  may  extend  from  frame  to  frame,  or,  as  is  more  often 
done,  for  a  sufficient  distance  on  each  side  of  bulkhead,  to  take  an- 
other row  of  rivets,  observing  that  these  holes  need  only  be  spaced 
for  watertight  riveting  on  the  caulking  side  of  bulkhead. 

Owing  to  the  water  pressures  being  greatest  on  the  bottom,  the 
plating  is  graded  in  thickness  towards  the  top,  and  of  course  the 
section  of  stiffening  bars  is  likewise  reduced.  The  lower  stiff eners 
require  bracketing  to  tank  top  ;  and  in  detailing  the  riveting  of 
these  brackets,  it  should  be  borne  in  mind  that  one  arm  takes 
tensile  and  the  other  shearing  stresses.  Watertight  spacing  is 
required  for  all  riveting  except  stiffeners  and  their  connections. 

Where  web  frames  or  deep  framing  is  substituted  for  hold 
beams,  additional  horizontal  stiffening  must  be  given  the  bulkheads 
at  the  level  at  which  the  lower  deck  would  ordinarily  support  the 
bulkhead,  and  in  addition  a  deep  centre  line  web  fitted. 

Generally  it  will  be  found  convenient  to  arrange  for  the  caulk- 
ing side  of  bulkhead  to  be  that  side  on  which  the  open  bevel  frame 
shows,  that  is,  the  after  side  in  fore-body  bulkheads,  and  the 
forward  side  in  after-body  bulkheads.  There  are  exceptions, 
however,  to  this  rule  which  will  suggest  themselves  in  considering 
deep  tank  and  peak  water  tests.  As,  of  course,  it  is  only  necessary 
to  caulk  one  side  of  the  bulkhead,  the  stiffening  bars  should  be 
arranged  on  the  opposite  side. 

Where  stiffening  bars,  especially  angles,  are  exposed  in  cargo 
holds  or  between  deck  spaces,  their  sharp  edges  must  be  protected 
by  fitting  wood  chafing  pieces  projecting  about  an  inch  and  a  half 
beyond  the  toe  of  bar  and  bolted  to  the  stiffening  flange. 

SHELL   PLATING. 

The  skin  of  the  ship  when  constructed  of  steel  is  almost  invari- 
ably arranged  in  fore  and  aft  strakes  "in"  and  "  out  "  alternately. 
For  the  reasons  given  when  treating  on  keels,  the  flat  plate  should 
be  fitted  as  an  "  in  "  strake,  so  also  should  the  sheerstrake  except 
in  large  steamers  where  a  doubling  is  required.  For  fitting  and 
shoring  purposes,  it  is  an  advantage  to  fit  the  bilge  strake  "  inside," 
as  well  as  strakes  adjoining  longitudinals. 

In  laying  off  the  widths  of  strake  on  the  midship  section,  it  will 
facilitate  interchangeability  of  individual  plates  if  all  strakes  of 
the  same  thickness  are  made  similar  in  width.  It  will  also  be 
found  advantageous  to  work  the  bilge  strake  narrower  than  the 


Shell    Plating 


3U1J 


others  where  an  odd  size  is  unavoidable.  In  moderate  sized 
vessels  the  outside  strakes  are  usually  from  40  to  it;  inches  wide, 
and  the  inside  ones  48  to  54  inches,  but  in  the  largest  ships  it  will 
be  good  practice  to  increase  these  widths,  although  by  so  doing 
increased  riveting  of  butts  will  be  necessary.  On  the  other  hand, 
when  dealing  with  small  vessels  or  light  scantling  craft  narrower 
plates  should  be  worked. 

The  widths  having  been  arranged  satisfactorily  on  the   midship 
section,  should  now  be  transferred  to  a  body  plan  and  run  in  to  the 

PLATE   LINES 


eye  as  shown  by  Fig.  101.  observing  that  in  the  fore  body  above 
the  waterline  the  widths  are  kept  parallel,  which  necessitates 
working  stealers  in  the  under-water  body  at  the  fore  end.  Run- 
ning these  plate  widths  parallel  gives  a  straight,  sharp  appearance 
to  the  sight  edges,  a  very  important  point  when  lining  off  a  very 
full  ship,   as  otherwise  the    rounding   up    lines   developed  would 


310 


The   Naval'  Constructor 


co 

\- 
^- 

CO 

u. 

o 

I- 
u. 

X 
CO 


FIQ.  192. 


Shell   Plating  311 

accentuate  and  exaggerate  the  bluff  lines.  In  addition  it  enables 
us  to  work  the  narrow  plates  where  the  form  is  most  difficult  to 
work.  In  the  after  body  different  conditions  exist,  the  most 
important  plate  line  being  that  which  ends  at  the  oxter,  so  that  it 
is  only  necessary  to  divide  the  space  intervening  between  that 
point  and  the  sheer  strake  into  the  number  of  strakes  obtaining 
amidships.  The  ending  of  a  plate-line  in  the  oxter  is  advisable  to 
obtain  all  the  furnacing  and  difficult  work  on  one  plate  only. 

Having  run  the  plate  lines  on  body  plan  to  fulfil  the  foregoing 
conditions,  these  may  then  be  taken  off  and  faired  up  on  the 
model. 

If  it  be  found  that  one  of  the  landings  crosses  the  continuous 
angle  of  tank  margin  plate  or  watertight  flat,  the  line  must  be 
stopped  abruptly  near  the  point  of  intersection  and  "jogged1' 
across  for  a  sufficient  distance  before  resuming  its  flight. 

Before  any  butts  whatever  are  laid  off,  either  for  stringers  or 
shell  plating,  a  small  diagram  should  be  drawn  giving  the  general 
scheme  for  the  shift  of  butts  which  will  enable  the  various  structu- 
ral plans  to  proceed  simultaneously  and  independently.  No  butts 
on  adjacent  strakes  should  be  placed  nearer  one  another  than  two 
frame  spaces,  or  one  frame  space  where  a  strake  intervenes.  The 
ideal  shift  of  butts,  however,  is  that  which  shall  have  not  more 
than  one  shell  butt  in  any  one  frame  space  from  keel  to  gunwale. 
After  the  shell  plate  butts  have  been  arranged,  those  of  stringers, 
longitudinals,  keelsons,  etc.,  may  be  set  off  in  the  best  positions  in 
relation  to  shell.  Such  plates  as  require  furnacing  should  be 
arranged  as  short  as  possible,  the  most  difficult  of  these  being  the 
"hip"  plate  on  the  quarters,  oxter  plate,  boss,  plate,  the  "breeches" 
plate  taking  stern  frame  and  plate  keel,  and  the  similar  plate  of 
spoon  form  forward  adjoining  the  stem.  In  some  forms  of 
vessels  it  is  also  advisable  to  make  a  short  plate  of  those  having 
double  set  at  fore  and  after  ends  of  bilge  where  the  latter  begins 
to  curve  into  the  entrance  and  run  of  vessel  respectively. 

A  scheme  of  butts  such  as  the  one  suggested  is  shown  by  the 
accompanying  diagram,  Fig.  192. 

The  "landings,"  as  the  edge  overlaps  of  the  in  and  out  strakes 
of  plating  are  called,  should  be  of  the  width  necessary  to  take  the 
required  size  of  rivets,  which  must  be  spaced  for  watertight  work, 
i.e.,  4  to  4\  diameters  apart,  observing  -that  where  double  riveting 
is  employed  a  single  rivet  only  should  be  inserted  at  the  closing, 
or  caulking  edge,  in  wake  of  all  frames.  In  yacht  construction 
where  a  perfectly  smooth  topside  is  desired,  the  plating  is  often 
arranged  edge-butt  fashion  with  an  inside  continuous  seam-strap  — 
a  more  expensive  and  less  efficient  method  than  the  other,  and 
adopted  solely  for  appearance. 

In  small  moderate  sized  vessels  the  garboard  and  sheerstrake 


312  The   Naval   Constructor 

landings  only  are  double  riveted,  but  in  large  vessels  all  of  the 
landings  should  be  provided  with  two  rows;  and  where  exceptional 
local  loads  are  carried,  as  in  deep  tanks,  or  in  vessels  above  480 
feet  in  length,  "  the  landing  edges  should  be  treble  riveted  for  one 
fourth  of  the  vessel's  length  in  the  fore  and  after  bodies  for  a  depth 
of  one  third  the  vessel's  depth."  Vessels  slightly  under  this 
dimension  may  have  double  riveted  landings  with  an  additional 
rivet  added  in  each  frame  space  within  the  zone  mentioned. 
Where  a  change  is  made  from  a  treble  to  a  double,  or  from  double 
to  single  riveted  landings,  the  taper  must  of  course  be  made  on  the 
inside  or  hidden  edge,  and  should  extend  over  a  frame  space. 

Individual  plates  of  strakes  should  be  fitted  in  as  long  lengths 
as  the  steel  makers'  limits  allow,  or  the  facilities  of  the  particular 
yard  permit,  consistent  always  with  good  practice.  The  old 
method  of  fitting  these  with  edge-butts  having  an  inside  covering 
strap  has  been  almost  entirely  superseded  by  overlapping  the  plates, 
a  stronger  and  more  enduring  method.  There  are  some  strakes 
and  special  cases,  however,  where  it  is  still  advisable  to  retain  the 
edge-butt  connection,  as  in  flat  plate  keels,  sheerstrakes  and  the 
strake  in  wake  of  bilge  keels,  as  by  this  means  we  get  a  closer  fit- 
ting for  keel  angles,  stringer  bars  and  mouldings  and  bilge  bars,  elim- 
inating unsightly  work,  trouble  and  the  expense  of  fitting   liners. 

Where  the  overlapped  landing  of  an  outside  strake  crosses  the 
buttlap  of  the  adjacent  inside  strake,  it  will  readily  be  seen  that  a 
small  wedge-shaped  space  is  formed.  To  close  this  up  and  so  ob- 
tain the  necessary  watertightness,  it  is  customary  to  scarph  the 
corner  of  the  overlap,  allowing  it  to  be  drawn  home.  In  wake  of 
the  outside  strake  overlaps,  where  they  adjoin  the  inside  landing 
edge,  planing  is  impracticable,  and,  as  a  similar  wedge-shaped 
aperture  interferes  here  also  with  watertightness,  this  is  secured 
by  fitting  a  tapered  liner  long  enough  to  take  three  rivets.  A 
similar  tapering  away  of  the  outside  landing  edge  is  performed 
where  the  strakes  end  on  stem  and  stern  post,  thus  giving  the  ap- 
pearance of  one  flush  thickness  at  these  parts. 

Wherever  the  shell  plating  is  cut  to  form  cargo  doors,  coal 
chutes,  sea  connections,  sidelights,  etc.,  compensation  must  be 
given  for  the  loss  in  strength  sustained.  More  especially  is  this 
imperative  where  these  openings  occur  amidships  through  the 
sheerstrake,  as  it  is  then  obvious  that  the  strength  is  reduced  to  a 
maximum,  being  at  the  extreme  fibres  and  where  the  greatest 
bending  moments  are  produced.  To  avoid  abrupt  discontinuities 
as  much  as  possible,  the  corners  of  all  such  holes  where  not  circu- 
lar should  have  a  bold  radius,  and  in  addition  kept  well  clear  of 
butts.  In  addition,  doubling  plates  must  be  fitted,  observing  that 
these  should  be  over  the  openings  and  encircling  the  upper  stresses 
acting  on  the  upper  corners,  as  the  stresses  acting  on  the  upper 


Detail    Fittings  313 


works  which  need  resisting  most  are  tensile.  Where  sidelights 
are  cut  through  the  sheerstrake,  compensation  may  be  given  by 
slightly  increasing  this  strake  in  thickness  or  by  fitting  compensat- 
ing angle-bars  over  the  openings. 

The  shell  plating,  as  will  be  seen,  really  forms,  in  conjunction 
with  the  strength  deck,  the  sides  and  bottom  and  top  members  re- 
spectively of  the  Bhip  v  tewed  as  a  box  girder.  For  this  reason  the 
parts  taking  the  greatest  stresses  are  those  at  the  greatest  distance 
from  the  neutral  axis  ;  and  as  a  ship  is  not  always  in  the  upright 
position  in  a  seaway,  it  will  be  evident  that  these  parts  are  the 
sheerstrake,  bottom  and  bilges.  Thus  tiie  classification  societies 
stipulate  for  thicker  plating  at  these  parts.  As  the  greatest  bend- 
ing moments  are  exerted  amidships,  diminishing  towards  the  ends, 
they  require  that  the  maximum  thickness  shall  be  retained  for  a 
quarter  of  the  vessel's  length  before  and  abaft  the  dead  fiat  frame. 
There  are,  however,  certain  localities  beyond  these  limits  where 
the  midship  thickness  must  be  maintained  if  not  increased  where 
abnormal  local  conditions  demand  it.  Conditions  such  as  are  re- 
ferred to  exist  at  the  ends  of  plates  adjoining  the  stern  frame, 
where,  besides  making  the  connection  to  a  heavy  forging  requir- 
ing very  large  rivets,  excessive  vibration  of  a  fatiguing  nature  is 
encountered  ;  and  at  the  bossed  plating,  oxter  and  hip  plates  re- 
quiring furnacing  and  much  consequent  hammering,  where  a  se- 
rious reduction  in  the  original  thickness  takes  place  in  addition  to 
the  distress  to  the  plate  consequent  on  the  treatment  to  which  it 
is  subjected.  Also  doubling  or  increased  thickness  must  be  pro- 
vided at  abrupt  breaks  in  the  longitudinal  strength,  as  at  ends  of 
poops  or  bridge  deck  superstructures,  in  wake  of  hawse  pipes,  etc., 
and  at  other  points  which  present  themselves  and  will  be  evident 
to  the  observant. 

DETAILS.     FITTINGS. 

Only  next  in  importance  to  the  structural  details  are  the  deck 
and  other  fittings,  on  which  the  convenient  and  safe  handling  of 
the  ship  depends.  These  in  many  cases  do  not  receive  that  consid- 
eration which  their  importance  merits.  Instead  of  being  calcu- 
lated on  a  rational  basis  and  designed  accordingly,  ship  fittings  are 
too  often  left  to  the  guesswork  of  the  technically  untrained,  with 
the  result  that  we  often  find  in  these  fittings  a  wide  variation  in 
the  scantliDgs  employed  for  a  given  duty  even  amongst  like  fittings 
oji  the  same  ship  where  different  sizes  are  used. 

With  the  object,  then,  of  proportioning  these  fittings  from  a 
rational  unit  and  standardizing  them,  the  following  tables  of  fit- 
ting details  have  been  prepared  or  collected.  The  basis  on  which 
the   unit  is  founded  is  in  many  cases  given,  enabling  the  expe- 


314 


The  Naval  Constructor 


Bill  of  Material 


:;  1 :, 


rienced  to  determine  for  themselves  whal  variation  may  safely  be 
made  where  fittings  are  being  designed  for  special  work. 

In  the  preparation  of  details  it  will  be  found  to  contribute  much 
to  their  elucidation  it  a  "  fitting  list "  or  '"bill  of  material"  be 
added  alongside  the  detail  delineated,  and  each  and  every  part  of 
the  fitting  given  a  special  "  piece  number."'  The  number  plan  of 
the  general  arrangement  on  which  the  details  are  assembled 
should  likewise  be  given,  and  of  course  these  piece  numbers  in- 
dicated on  this  assembly  drawing  for  identification.  The  piece 
numbers  will  also  prove  helpful  as  reference  numbers  in  discus- 
sions or  correspondence  relating  to  the  particular  fitting. 

The  adjoining  specimen  plate,  with  its  accompanying  bill  of  mate- 
rial, has  been  prepared  to  illustrate  the  method  advocated. 


BILL   OF   MATERIAL   FOR    ONE   BOAT. 


S 

—  — 

— 

?. 

•- 

- 
6 

y.  t 

t  a 

^  o 

Name. 

■ 
-  J 

=  « 

'-     — 

►a 

o 
y 

— 
— * 

44  ft. 

Pat.  79 

M.  C.  I. 

86-370 

12 

7 

Die  670 

Rail  stanchion   .... 

W.  I. 

<< 

TO 

8 

"     673 

it                   (( 

W.I. 

it 

26  yd. 

12 

.... 

Red  metal 

it 

12 

23 

Pat.  103 

Thumb  screw     .... 

Comp.  X. 

ii 

43 

42 

.... 

Brass 

5* 

14 

56 

93 

Die  685 

Bye  bolt 

W.  I. 

— 

II 

28 

94 

•     •     •     • 

1"  W.  I.  gas  pipe  sleeve, 

W.I. 

**- 

it 

58 

95 

W.  I. 
(galv'd.) 

-5 

II 

74 

96 

Die  691 

Eye  in  end  of  rail  .    .    . 

W.  I. 

g 

(I 

810  ft. 

97 

*     •     >     • 

\\"  rod  (top  rail)     .     .    . 

W.  I. 

II 

2,365  " 

98 

.... 

1"  rod  (middle  and  lower 

W.  I. 

II 

88 

170 

.... 

H"  tap  bolt 

W.  I. 

II 

86 

171 

Die  675 

Kail  stanchion    .... 

W.  I. 

u 

44 

172 

"     676 

i<            << 

W.I. 

ii 

316 


The  Naval  Constructor 


STANDARD    HATCHING   FOR    VARIOUS 

MATERIALS. 


ALUMINIUM 


LEAD  OR   BABBITT 


BRASS,    COMPO 
OR    BRONZE 


BLUE         U.S. 


■!,■■,— 


GREY  U.S. 


CAST    IRON 


CAST   STEEL 
OR    MALLEABLE    IRON  WROT.    IRON 


WROT.    STEEL 


WIRES 

in+iuuji'.J.ui.M 


.*,*- 


WOOD 

l 

- - 

-■" 

CELLULOSE 


GLASS 


U.S. 


YELLOW   &   BRQWN 
ILSi 


GREEN  &  WHITE     U.8. 


LEATHER 
GUM   OR   RAW   HIDE 


VULCANITE 


CEMENT 

W 

W////A 

m. 

YELLOW   &    RED 
U.S. 


YELLOW    BROWN   & 
GREEN  U.8. 


.-': 


a^^'v^r^ 


^^^ 


YELLOW,    BROWN   &   GREEN 


u.s. 


Figs.  194-211. 


Graphic    Division   of  One    Inch  317 


GRAPHIC    DIVISION    OF    ONE    INCH. 


1  INCH  DIVIDED  INTO 


STEEL  PLATES 

LBS.  PER  SQ. 

FT. 

16™s 

' 

32NDS. 

4QTHS 

MILLIMETERS. 

IRON  PLATES 

LBS.  PER  SQ. 

FT. 

40.80 

'6 

20 

32 

40 

40 

— 

—          — 

—             — 

25 

f 

38.76 

—       30     — 

38 

24 

38 

1 

14 

18 

i 

36.72 

36 

36 

28 

22 

34.63 

— 

. — .            — 

34 

34 

— 

i 

_ *    16 

26 

i 

32.64 

32 

20 

32 

12 

—             — 

—              _ 

30.60 

24 

30 

30 

— 

14 

—              — 

i 

28.56 

22 

23 

18 

28 

—              — 

' — 

10 

26.52 

26 

~~      16 

26 

—     20 

i 

24.43 

12 

■ —             - — 

24 

24 

—              — 

18 

—      14 

22.14 

22 

22 

8 

10 

— 

20.40 

16 

20 

20 

b 

—     12 

—              — I 

—             — 

z 

18.36 

14 

18 

18 

^ 

8 

16.32 

6 



16 

—     10 

16 

12 

14.28 

— 

—             — 

14 

14 

6 

—      8 

12.24 

1  u 

12 

12 

4 

— 

—              — 

10.20 

—     8     — 

10 

—      6 

10 

4 

—           — 

— 

8.16 

6 

8 

8 

—              — 

2 

6.12 

6 

4 

6 

4 

— 

4.08 

2 

—             — 

4 

4 

1 

1 

2 

2.04 

2. 

2 

1 

2 

1.02 

1 

1 

1 

1 



1 

318 


The  Naval  Constructor 


BALDT   ANCHOR. 


Fig.  212. 


Dimensions   of  Baldt   Stockless   Anchors      319 


DIMENSIONS    OF    BALDT    STOCKLESS    ANCHORS. 

(Cast  Steel.) 
Weight  in  Pounds. 


Lbs. 

5,600 

5,400 

1,760 

2,940 

1,820 

1,680 

840 

i 

rt 

n 

a 

// 

a 

// 

A 

23 

23 

21 ; 

20 

171 

16* 

14 

B 

16 

16 

15* 

14 

10 1 

io  i 

9 

C 

10 

10 

10 

•■•:■ 

6 

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n 

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7* 

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n 

m  -i 

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61 

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9 

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9 

9 

8 

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G 

60 

60 

56  \ 

50J 

44* 

41 

33i 

H 

35 

35 

33* 

3(i  1 

25  * 

25  \ 

20 

I 

53 

53 

5]  J 

45] 

31  g 

37  | 

30  | 

J 

161 

16| 

15i 

i;;i 

10 1 

10  f 

81 

K 

12 

12 

Hi 

31 

7 

7 

6 

L 

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7 

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6i 

6 

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231 

23J 

21i 

20 

15  \ 

15  i 

121 

0 

2| 

- 

3 

- 

2* 

11 

If 

p 

16| 

16| 

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15J 

ii  j 

11* 

91 

Q 

6 

6 

H 

•  > 

4  L 

4  £ 

3 

B 

72 

72 

72 

66 

54 

54 

40 

8 

8f 

8! 

8i 

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<n 

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T 

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6f 

5£ 

U 

5 

6 

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d 

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6 

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8 

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Th 

I 

5i 

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*  ] 

CWT. 

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48} 

42* 

2*\ 

m 

15 

7* 

320 


The   Naval   Constructor 


HALL    ANCHOR. 


f*~G-T-4« — &--*! 
Fig.  213. 


Dimensions  of  Hall   Anchors 


321 


DIMENSIONS    OF    HALL    ANCHORS. 


*  ^ 

~ 

., ,  _* 

-.* 

— ' 

■ 

— • 

:-    •*  00 
*■    —  ~~ 

~  -  /■ 

II 

■ 

e 

li 

1.93 

— 

II 

— 

-r 

ii 

ii 

— 
5C 

39 

II 

3 

00 

f 

II 

t- 

— 

Jl 

1 

-1 

II 

-i 

:: 

II 

'< 

10.47 

— 

II 

< 

i  - 

ii 

165 

3.07 

4.92 

1.26 

2.64 

29.53 

14.76 

3.62 

7.36 

4.06 

2. 'JO 

220 

3.39    2.09 

5.43 

1.38 

2.91 

32.52 

16.26 

3.98 

8.11 

11.54 

4.49 

2.44 

330 

3.86    2.36 

6.18 

1.57 

3.31 

37.05 

1-.-.4 

4.53 

9.25 

13.15 

5.12 

2.80 

440 

4.25 

2.64 

6.81 

1.73 

3.66 

40.00 

20.43 

5.00 

10.20 

14.49 

5.63 

3.07 

550 

4.61 

2.87 

7.36 

1.89 

3.94 

40.28 

22.13 

5.43 

11.06 

15.71 

6.10 

3.31 

660 

4.88 

3.03 

7.80 

2.00 

4.17 

46.90 

23.47 

5.75 

11.73 

16.65 

0.40 

3.50 

880 

5.35 

3.35 

8.54 

2.2t» 

4.61 

51.42 

25.71 

6.30 

12.87 

18.27 

7.09 

3.86 

1,100 

5.79 

3.58 

9.25 

2.40 

4.96 

55.63 

27.80 

6.81 

13.90 

19.72 

7.68 

4  17 

1,320 

6.14 

3.82 

9.80 

2.52 

5.28 

59.02 

29.40 

7.24 

14.70 

20.95 

8.11 

4.41 

1,540 

6.46    4.02 

10.32 

2.68 

5.55 

62.02 

30.91 

7.60 

15.51 

22.00 

8.54 

4.65 

1,765 

0.77    4.21 

10.83 

2.80 

5.79 

05.04 

32.52 

7.95 

16.26 

23.11 

8.98 

4.88 

1,985 

7.05    4.37 

11.26 

2.91 

6.02 

07.08 

33.86 

8.27 

16.93 

24.00 

9.33 

5.12 

2,200 

7.28 

4.53 

11.65 

2.99 

6.26 

09.96 

35.00 

8.58 

17.48 

24.88 

9.65 

5.28 

2,700 

7.83 

4.88 

12.56 

3.23 

6.73 

75.28 

37.64 

9.21 

18.82 

26.73 

10.35 

5.67 

3,310 

8.35 

5.20 

13.35 

3.43 

7.17 

SO.  10 

40.42 

9.80 

20.04 

28.54 

11.02 

6.02 

3,8G0 

8.78 

5.47 

14.00 

3.62 

7.52 

84.33 

42.50 

10.35 

21.06 

29.96 

11.61 

6.34 

4,410 

9.17 

.-..71 

14.09 

3.78 

7.87 

88.47 

44.39 

10.79 

22.00 

31.30 

12.13 

0.05 

4,900 

9.53    5.95 

15.24 

3.94 

8.15 

91.54 

46.09 

11.22 

22.87 

32.52 

12.60 

6.89 

5.510 

9.88    0.14 

15.79 

4.06 

8.46 

94.92 

47.82 

11.61 

23.74 

33.70 

13.07 

7.13 

6,610 

10.51 

10.81 

4.33 

9.02 

100.99 

50.81 

12.30 

25.24 

35.87 

13.90 

7.60 

7,720 

11.06 

6.89 

17.68 

4.57 

9.49 

106.26 

53.49 

13.03 

26.58 

37.7.; 

14.65 

7.95 

8,820 

11.58 

7.20 

18.50 

4.76 

9.92 

111.30 

55.93 

13.62 

27.80 

39.83 

15.32 

8.35 

9,920 

12.00 

7.48 

19.21 

4.96 

10.28 

115.36 

58.02 

14.13 

41.32 

15.91 

8.66 

11,020 

12.44 

7.76 

19.88 

5.12 

10.67 

120.28 

60.06 

!  1.65 

29.88 

42.78 

16.46 

8.98 

13,230 

L3.23 

21.14    5.43 

11.34 

127.09 

63.88 

15.55 

31.77 

15.46 

17.:.  2 

9.57 

322 


The   Naval   Constructor 


ADMIRAL    ANCHOR. 


fr 


r 


«Q 


m 


L 


Fig.  214. 


Admiral  Anchor 


323 


ADMIRAL    ANCHOR. 


9,240 

7.840 

3,080 

1, 

:m 

6, 

.04 

5,180 

1,792 

910 

/    // 

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/          // 

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rt 

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59 

4    6 

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5 

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4  11 

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2    9 

2  7 

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1    6 

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324 


The    Naval   Constructor 


INGLEFIELD    ANCHOR. 

Unit  A"  =  .5G93V  W,  where  W  =  weight  in  lbs. 


A  -=i  unit  in  inches, 
B  =  9.5  A. 
C=2.5  A. 
J)  =1.25  A. 
E=  .6  A. 
F  =    .37  A. 


G  =  2.2i  A. 
H=  .624  A. 
1=  .773  A. 
K=  .70  X 
L=  .50  ^4. 
Af=    .85     A. 


Fig.  215. 


Anchor  Crane  Stresses 


o20 


33V- - 


ANCHOR  CRANE 


Fig.  216. 


DOUBLE 
3LOCK 


DITTO 


Compression  on  jib 


Q  —  Load  in  tons. 

W=  Weight  of  jib  and  tie  rods  in  tons. 
d  =  Spread  in  feet. 
Tension  on  tie  rods  = 

Q  _  Q  x  d  +  W  x  e 

Qxd+We+QiXh 

i  —  — 

9 

If  arrangement  of  blocks  as  shown,  then 

To  calculate  dimensions  of  crane  post,  the  horizontal  resultant 
poles  of  S  and  T  should  be  used,  as  : 

>'i  =  S  x  cos  a. 

Tx  =  T  X  cos  /3. 
Pi  and  Po  represent  the  shearing  stresses  at  the  points  A  and  B. 

_  _  S,  (a  +  b)-T,  6 


„       S!  (a  +  6+0-^(6 +  c) 


326 


The  Naval  Constructor 


</) 


a. 


O'      VB 


a 


~*j»|~ 


-o 


C      B  x 

DIAGRAM  OF  BENDING  MOMENTS 

Fig.  217. 

Bending  Moment  on  Crane  Post. 

At  B,  MB  —  Pi  x  c  Foot-tons.  At  A%  Mx  —  0. 

At  C,  ifc=  Pi  x  (6  + c)-P2x&.        At  7),  MD  =  0. 


Diagram  of  Bending  Moments. 

Draw   vertical   lines  at   B  and    C  representing  the  moments 
MB  and  Mc,  and  complete  the  figure  as  shown  on  sketch. 

From  this  diagram  the  moment  MK  at  any  point  x  may  be  scaled. 


Graphic  Method  to   Determine  T  and  S 


327 


GRAPHIC  METHOD 
TO  DETERMINE 

"T"&."S,J 


Fig.  218. 


Graphic  Method  of  Determining  T  and  S. 

Q  =  load  in  tons. 

W  =  weight  of  jib  and  tie  rods  in  tons. 

Draw  at  the  point  E  a  vertical  line  EF  —  Q. 

From  F  draw  FG  parallel  to  ED,  then  EG,  increased  with  the 
projection  of  W  and  Q,  in  the  direction  of  the  jib  will  represent  to 
scale  the  compression  T. 

The  line  FG  =  EH,  increased  with  the  projection  of  W  in  the 
direction  of  the  tie  rods,  will  represent  the  tension  S. 


328 


The  Naval   Constructor 


DIMENSIONS    OF  ANCHOR    CRANES. 


H  O  |j  f_ 
W  W  K  W 

** 

^  R 

One 

Two 

<  * 

One 

Two 

§XM 

Tie 

Tie 

Jib. 

2£*vw 

H    H 

Tie 

Tie 

Jib. 

02   W 

Rod. 

Rods. 

02     W 

Rod. 

Rods. 

Foot- 
cwts. 

Dia. 

Dia. 

Dia. 
eacli. 

Dia, 
mid- 
dle. 

Foot- 
cwts. 

Dia. 

Dia. 

Dia. 
each. 

Dia. 
mid- 
dle. 

n 

// 

// 

a 

a 

a 

a 

180 

6 

If 

1    8 

3 

540 

8| 

2f 

If 

4i 

200 

6i 

t  t 

1 1 

it 

550 

ti 

it 

it 

if 

220 

6* 

n 

la 

1  a 

3i 

560 

it 

it 

ti 

ft 

225 

it 

(i 

tt 

tt 

585 

9 

1\ 

113 
1T5 

4* 

240 

6f 

tt 

tt 

tt 

600 

ti 

tt 

ti 

ti 

250 

ti 

ii 

tt 

it 

605 

it 

tt 

tt 

ti 

260 

ti 

it 

tt 

it 

630 

H 

it 

ii 

ii 

270 

7 

2 

H 

3i 

650 

tt 

ti 

ti 

it 

275 

i< 

tt 

it 

l" 

660 

ti 

tt 

it 

it 

280 

tt 

(i 

<t 

it 

675 

9J 

2f 

2 

4| 

295 

1\ 

tt 

tt 

tt 

700 

tt 

tt 

ii 

it 

300 

(( 

tt 

it 

tt 

715 

it 

ti 

tt 

tt 

325 

tt 

tt 

tt 

tt 

720 

tt 

tt 

ti 

tt 

330 

73 

91 

"8 

1 9 

3|    . 

750 

9| 

tt 

tt 

tt 

350 

t*i 

tt 

tt 

tt 

770 

1 1 

ti 

it 

ii 

360 

ti 

tt 

tt 

tt 

780 

ii 

tt 

ti 

it 

375 

7| 

tt 

it 

ti 

825 

10 

2f 

0  1 

"15 

5 

385 

14 

tt 

tt 

tt 

840 

tt 

tt 

tt 

ti 

390 

it 

tt 

tt 

it 

900 

101 

it 

it 

it 

400 

[< 

It 

it 

it 

1,000 

10£ 

2| 

91 

*•  8 

54 

405 

8 

91 

IS 

-1  a 

4 

1,100 

10| 

ii 

tt 

ii 

420 

ft 

tt 

tt 

tt 

1,200 

m 

tt 

tt 

ti 

440 

tt 

tt 

tt 

tt 

1,300 

ii 

3 

2i 

5* 

450 

8J 

tt 

tt 

it 

1,400 

in 

ti 

i  4 

ti 

455 

if 

tt 

tt 

tt 

1,500 

114 

ti 

tt 

tt 

480 

(f 

tt 

tt 

tt 

1,600 

1H 

3§ 

2f 

5f 

490 

tt 

it 

tt 

i> 

1,700 

HI 

it 

ti 

ti 

495 

si 

22 

1  S 
1  4 

4} 

1,800 

HI 

3i 

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*  2 

53 

500 

&( 

tt 

ti 

ft 

1,900 

HI 

ii 

ti 

tt 

525 

k 

tt 

it 

it 

2,000 

12 

3| 

It 

6 

Anchor    Cranes  329 


NOTES    ON   ANCHOR    CRANES. 

The  most  suitable  radius  of  crane  to  efficiently  fish  the  anchor 
having  been  determined,  this  dimension  in  feet  multiplied  by  the 
weight  of  anchor  including  stock,  will  give  the  moment  in  foot- 
c\vts. ,  to  which  reference  must  be  made  for  the  corresponding  sizes 
of  parts. 

N.B. — These  cranes  are  in  accordance  with  Lloyd's  require- 
ments per  Table  12,  but  for  convenience  the  moment  is  given, 
which  will  be  found  much  easier  of  application,  and  the  table  has 
been  extended  to  deal  with  the  heaviest  anchors. 

Of  course  where  the  ship  is  not  classed  to  Lloyd's,  the  crane 
should  be  figured  out  with  a  factor  of  safety  of  eight,  when  it  will 
be  found  that  the  sizes  in  this  table,  being  empirical,  may  be  con- 
siderably reduced. 

The  heavier  sizes  of  cranes  may  with  economy  be  built  up  with 
structural  sections,  or  the  post  and  jib  may  be  formed  with  angle 
sections  having  lattice  bracing. 

It  will  also  be  found  more  economical  to  step  the  crane  post  or 
anchor  deck  in  preference  to  housing  it  and  making  it  revolve 
with  the  jib. 


330 


The   Naval   Constructor 


BRONZE    SHIP'S    BELL. 

Copper  13,  Tin  4  parts. 

Directions  for  Laying  Out.  —  Divide  diameter  of  bell  into 
24  parts. 


\\\  SHIP'S  BELL. 


{y 


^\  \ 


\ 


■  C  toC-=Vz 

I        // 


- 


7 


Then 


(/> 

as/ 

/7/B 

//  /  i 

if/  ■ 

\| 

1 

/ 

K4    "--. 

h~ 

Fig. 219. 

I 

ylZ)  =    6  parts. 
DB=U     " 

6  —  &  =11  parts. 
A -4  =   4         " 

if- 5  =14     " 

P  —  Q  =     tl  diam. 

B-H=U     " 
.C-c  =     |  " 

Bad.  K  =  3  |  parts. 
.4—8=8        " 

c-b  =    hi  « 

Thickness  at  8  =           part. 

6-s  =11 

it 

Arc  J.  —  #,  drawn  with  rad.  of  3|  parts  from  K,  wherever  that 
may  fall,  the  rest  of  curve  laid  in  by  hand. 

Rad.  of  crown  17  parts  may  be  16J  to  19;  thickness  of  bell  at  J5, 
|  parts  =  waist,  sound  bow  =  -^  diam.  =  QP. 

Part  of  bell  above  bis.  laid  in  as  a  cylinder. 


Belay   Pins 


331 


WEIGHT    OF   BRONZE    SHIP'S   BELLS. 


Diameter 

of  Mouth  nr 

Inches. 

Weight  nr 
Pounds. 

Diameter 

of  Mouth  in 

Inches. 

Weight  in 
Pounds. 

6 

7 

8 

9 

10 

11 

12 

13 

14 

6 
8 
10 
15 
18 
22 
26 
38 
55 

15 
16 
17 
18 
19 
20 
21 
22 

65 
75 
100 
125 
156 
178 
204 
231 

Note.  —  Weights  given  are  exclusive  of  hangers  or  belfry. 


BELAY   PINS. 

»f« B- 


FlG.  220. 


Size 

of 

A. 

B. 

C. 

D. 

E. 

F. 

G. 

Pin. 

n 

a 

a 

a 

a 

a 

// 

a 

i 

4 

5 

7 

h\ 

9 

n 

i 

f 

H 

6 

15 
T* 

1A 

1  1 
IT 

n 

i 

1 

5 

7 

1 

If 

l  s 

T6 

1A 

n 

i 

•H 

8 

It1* 

n 

w 

1A 

M 

1 

6 

9 

H 

iH 

ItV 

n 

if 

H 

6f 

10 

n 

H 

iA 

M 

2 

H 

n 

11 

IfV 

2 

ifV 

H 

2i 

if 

8 

12 

if 

2tV 

1    7 
iT* 

i| 

2* 

l* 

8* 

13 

i* 

2| 

1    9 

m 

2f 

332  The  Naval  Constructor 


SHIP'S   BOLLARDS    (STANDARD). 

Bollards  are  invariably  made  of  cast  iron  of  good  quality,  and 
should  be  fairly  smooth  castings.  In  small  yacht  and  high  class 
work  they  are  sometimes  made  of  gunmetal,  and  in  battleships  of 
steel.  The  bolt  holes  should  not  be  cored  but  drilled  and  counter- 
sunk afterwards,  the  bolts  being  of  BB  iron  or  steel  with  full 
countersunk  heads. 

The  diameter  B  of  the  barrel  should  be  in  accordance  with 
the  sizes  given  in  the  table,  opposite  the  corresponding  length  of 
vessel,  and  with  this  dimension  as  a  unit  the  proportionate  sizes 
of  the  various  parts  calculated  from  the  appended  proportion 
table  and  diagram  : 


v&j 


Diameter  of  bollard B—l. 

Centres C  =  2.83 

Height #  =  1.77 

Length Z  =  5.22 

Width  of  base ir=1.50 

Ends £=1.20 

Diameter  of  top D=1.16 

Depth  of  ridge E  =    .33 

Thickness  of  base T=   .17 

Thickness  of  side S  =    .  12 

Moulding  at  top If  =   .16 


Standard   Bollards 


333 


STANDARD  BOLLARDS 


-*1 


Via.  221. 


TABLE    OF  BOLLARDS    (Cast  Iron). 


Length 

Dimen- 

Approxi- 

Length 

Dimen- 

Approxi- 

Ship. 

sion  B. 

H  \TE 

Weight. 

of 
Ship. 

sion  B. 

M  \  TE 

Weight. 

Ft. 

Ins. 

Lbs. 

Ft. 

Ins. 

Lbs. 

60 

3 

40 

420 

13£ 

1,710 

80 

«5 

50 

440 

14 

1,900 

100 

4 

60 

460 

14| 

2,100 

110 

H 

72 

480 

15 

2,310 

120 

5 

85 

500 

16* 

2,525 

140 

5$ 

110 

520 

16 

2,750 

160 

6 

145 

540 

16* 

3,000 

170 

6* 

185 

560 

17 

3,250 

180 

i 

235 

580 

17i 

3,540 

190 

n 

295 

600 

18 

3,850 

200 

8 

360 

620 

18* 

4,140 

210 

8* 

430 

640 

19 

4,440 

220 

9 

510 

660 

19* 

4,810 

240 

o* 

605 

680 

20 

5,160 

280 

10 

700 

700 

20  \ 

5,560 

300 

10* 

815 

720 

21 

5,960 

320 

11 

935 

740 

21* 

6,390 

340 

n* 

1,070 

7  60 

22 

6,780 

360 

12 

1,210 

780 

22  * 

7.240 

380 

12* 

1,375 

800 

23 

7,6(50 

400 

13 

1.530 

850 

24 

8.560 

N.B.— The  extra  heavy  bollards  on  forecastle  head  and  quarters  should 
be  £  larger  than  given  in  table  for  the  corresponding  length  of  ship. 


334 


The   Naval   Constructor 


STANDARD   BLOCKS    i 

^Chain 

Sheaves). 

Single. 

Double. 

5 

10 

15 

20 

5 

10 

15 

20 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

il 

if 

a 

a 

// 

// 

a 

a 

A 

*l 

n 

9 

11 

4f 

74 

9 

11 

B 

3 

44 

5£ 

7  4 

*    4 

O 

44 

51 

74 

C 

4  S 

*  8 

7A 

10  i 

13 

4  2 

*  8 

7TV 

10  4 

13 

D 

3 

4i 

54 

64 

3 

44 

54 

64 

E 

41 

34 
6| 

5# 

6f 

104 

44 

F 

"  8 

34 

G 

3  8 

2J- 

9  7 

H 

2fV 

9   7 

34 

44 

I 

1  h 

11 

2  5 

J 

-1  2 

H* 

*   8 

24 

K 

14 
if 

24 

113 

2  f 

3| 

2| 

L 

2 

M 

1* 

2A 

21 

4 

N 

l-9- 

2| 

14 

If 

2| 

2 

3  A 

0 

al  6 
7 

u  2 

24 
24 

P 

8 

*A 

2 

Q 

9 
16 

13 

-16 

13 

16 

I 

R 

}A 

1    7 

2 

2| 

S 

}A 

1  I 

2 

2f 

T 
U 

4 

5 

6 
4 

8 
i 

10 

4 

V 

5 
16 

J 

a 

8 

4 

W 

3f 

&A 

7f 

Q  5 
"iff 

X 

3A 

*4 

n 

74 

Y 

2. 
T 

14 

H 

14 

Z 

1* 

2 

2f 

34 

a 

5 
16 

5 
8 

5 

8 

3 
4 

b 

5 

8 

5. 

8 

5 

8 

8 

5 

8 

5 
8 

5 

8 

ft 

c 

1  a 

1  8 

m 

24 

2H 

l-9- 

•••16 

2A 

2-7- 

244 

d 

1  g 

x  8 

2i 

24 

34 

lit 

24 

9  3 

Z  8" 

3 

e 

a* 

3 

34 

4  i 

*Tff 

2A 

9   5 

Z   8 

Ol  3 
ZT6 

34 

f 

n 

2A 

«A 

9  5 

^  8 

H 

9_5_ 

^16 

9   3 

2  £ 

^  8 

9 

2f 

3| 

3  § 

°  8 

5 

31 

ft  5 

6 

74 

h 

3 

5 

9 
16 

5 

8~ 

1 

3 

8 

9 
16 

1 

* 

i 

ItV 

14 

1  & 

1  8 

2A 

1A 

14 

If 

2fV 

k 

1t56 

1H 

2 

9  i 

ly56 

HI 

2 

9  i 

I 

4 

U 

11 

1  £ 

1  8 

I 

U 

U 

If 

m 

5 

8~ 

ItV 

11 

14 

5 

8 

1A 

14 

14 

n 

•         •        • 

1A 

1A 

144 

116 

1A 

1A 

1A 

HI 

Standard    Blocks 


335 


STANDARD  BLOCKS 


k— d— 

Figs.  222-225. 


336 


The   Naval   Constructor 


UNITED    STATES    STANDARD 


Bolt. 

Diameters. 

Thickness. 

Areas. 

u 

© 
ft 

P 

.Av 

O      • 

"3 

n 

( 

1 

4a 

s 

s 

u  " 

3 

H 

4 

is 

n 

«-4 

1 

O  u 

.25 

20. 

.5 

.578 

.707 

.1850 

.25 

.25 

.0491 

.0269 

.3125 

18. 

.5938 

.686 

.840 

.2403 

.3125 

.2469 

.0767 

.0454 

.375 

16. 

.6875 

.794 

.972 

.2938 

.375 

.3438 

.1104 

.0678  ! 

.4375 

14. 

.7813 

.902 

1.105 

.3447 

.4375 

.3906 

.1503 

.0933 

.5 

13. 

.875 

1.011 

1.237 

.4001 

.5 

.4375 

.1963 

.1257 

.5625 

12. 

.9688 

1.119 

1.370 

.4542 

.5625 

.4844 

.2485 

.1621 

.625 

11. 

1.0625 

1.227 

1.502 

.5069 

.625 

.5313 

.3068 

.2018 

.75 

10. 

1.25 

1.444 

1.768 

.6201 

.75 

.625 

.4418 

.3020 

.875 

9. 

1.4375 

1.660 

2.033 

.7307 

.875 

.7188 

.6013 

.4193 

1. 

8. 

1.625 

1.877 

2.298 

.8376 

1. 

.8125 

.7854 

.5510 

1.125 

7. 

1.8125 

2.093 

2.563 

.9394 

1.125 

.9063 

.9940 

.6931 

1.25 

7. 

2. 

2.310 

2.828 

1.0644 

1.25 

1. 

1.2272 

.8899 

1.375 

6. 

2!  1875 

2.527 

3.093 

1.1585 

1.375 

1.0938 

1.4849 

1.0541 

1.5 

6. 

2.375 

2.743 

3.358 

1.2835 

1.5 

1.1875 

1.7671 

1.2938 

1.625 

5.5 

2.5625 

2.960 

3.623 

1.3883 

1.625 

1.2813 

2.0739 

1.5149 

1.75 

5. 

2.75 

3.176 

3.889 

1.4902 

1.75 

1.375 

2.4053 

1.7441 

1.875 

5. 

2.9375 

3.398 

4.154 

1.6152 

1.875 

1.4688 

2.7612 

2.0490 

2. 

4.5 

3.125 

3.609 

4.419 

1.7113 

2. 

1.5625 

3.1416 

2.3001 

2.25 

4.5 

3.5 

4.043 

4.949 

1.9613 

2.25 

1.75 

3.9761 

3.0213 

2.5 

4. 

3.875 

4.476 

5.479 

2.1752 

2.5 

1.9375 

4.9087 

3.7163 

2.75 

4. 

4.25 

4.909 

6.010 

2.4252 

2.75 

2.125 

5.9396 

4.6196 

3. 

3.5 

4.625 

5.342 

6.540 

2.6288 

3. 

2.3125 

7.0686 

5.4277 

3.25 

3.5 

5. 

5.775 

7.070 

2.8788 

3.25 

2.5 

8.2958 

6.5092 

3:5 

3.25 

5.375 

6.208 

7.600 

3.1003 

3.5 

2.6875 

9.6211 

7.5491 

3.75 

3. 

5.75 

6.641 

8.131 

3.3170 

3.75 

2.875 

11.0447 

8.6412 

4. 

3. 

6.125 

7.074 

8.661 

3.5670 

4. 

3.0625 

12.5664 

9.9929 

4.25 

2.875 

6.5 

7.508 

9.191 

3.7982 

4.25 

3.25 

14.1863 

11.3302 

4.5 

2.75 

6.875 

7.941 

9.721 

4.0276 

4.5 

3.4375 

15.9043 

12.7405 

4.75 

2.625 

7.25 

8.374 

10.252 

4.2551 

4.75 

3.625 

17.7205 

14.2205 

5. 

2.5 

7.625 

8.807 

10.782 

4.4804 

5. 

3.8125 

19.6350 

15.7659 

5.25 

2.5 

8. 

9.240 

11.312 

4.7804 

5.25 

4. 

21.6475 

17.5745 

5.5 

2.375 

8.375 

9.673 

11.842 

4.9530 

5.5 

4.1875 

23.7583 

19.2678 

5.75 

2.375 

8.75 

10.106 

12.373 

5.2030 

5.75 

4.375 

25.9672 

21.2620 

6. 

2.25 

9.125 

10.539 

12.903 

5.4227 

6. 

4.5625 

28.2743 

23.0947 

n:,motor„t  f Sharp    V    of    60°    angle  =  Diameter  bolt  less 

RmtTn™  J         (1.73205  X  pitch  of  thread). 

m PThri«ri  I  "Sellers"    or    .75  depth  of  thread  =  Diameter   bolt    less 

01  j.nreaa.  ^    (1.2990375  x  pitch  of  thread). 

Flats  of 


[0|  or   yy   nuts  =  1.5  diameter  of  bolt  +  .125" 
Corners  of  foi  nuts  =:  1.155  flats, 


United   States   Standard   Bolts  and   Nuts     337 


BOLTS    AND    NUTS,   ETC. 


Tensile  Si  ki:m;th. 

Shearing  Strength. 

OS 

=>d 

M 

- 
Z. 

in 

u 

5    I 

Full  Bolt. 

Bottom  of 
Thread. 

,000  lb; 
Sq.  In. 

'"7. 

—  a 

8~ 

L"-X 

00 

8gfl 

0,000 

s. 

q.  In. 

so 

8  fefl 

—  ■ 

o 

4a 

■-"£  J. 

5    cc 

% 

< 

"< 

< 

^        CU 

< 

& 

269 

336 

471 

368 

491 

202 

269 

No.  14 

454 

568 

795 

575 

767 

341 

454 

"    14 

678 

848 

1,187 

828 

1,104 

509 

678 

"    13 

933 

1,166 

■    1,633 

1,127 

1,503 

700 

933 

"    13 

1,257 

1,571 

2,200 

1,472 

1,963 

943 

257 

"    12 

1,621 

2,026 

2,837 

1,864 

2,485 

1,216 

1,621 

"    12 

2,018 

2,523 

3,532 

2,301 

3,068 

1,514 

2,018 

"    11 

3,020 

3,775 

5,285 

3,314 

4,418 

2,265 

3,020 

"    10 

4,193 

5,241 

7,338 

4,510 

6,013 

3,145 

4,193 

"      9 

5,510 

6,888 

9,643 

5,891 

7,854 

4,133 

5,510 

"      8 

6,931 

8,664 

12,129 

7,455 

9,940 

5,198 

6,931 

"      7 

8,899 

11,124 

15,573 

9,204 

12,272 

6,674 

8,899 

"      6 

10,541 

13,176 

18,447 

11,137 

14,849 

7,906 

10,541 

"      5 

12,938 

16,173 

22,642 

13,253 

17.671 

9,704 

12,938 

ii      4 

15,149 

18,936 

26.511 

15,554 

20,739 

11,362 

15,149 

"      3 

17.441 

21,801 

30,522 

18,040 

24,053 

13,081 

17,441 

"      2 

20,490 

25,613 

35,858 

20,709 

27,612 

15,368 

20,490 

"      1 

23,001 

28,751 

40,252 

23,562 

31,416 

17,251 

23,001 

"      1 

30,213 

37,766 

52,873 

29,821 

38,761 

22,660 

30,213 

37,163 

46,454 

65,035 

36,815 

49,087 

27,872 

37,163 

6   // 

is 

46,196 

57,745 

80,843 

44,547 

59,396 

34,647 

46,196 

1" 

54,277 

67,846 

94,985 

53,015 

70,686 

40,708 

54,277 

2" 

8 

65,092 

81,365 

113,911 

62.219 

82,958 

48,819 

65,092 

[ill 

75,491 

94,364 

132,109 

72,158 

96,211 

56,618 

75,491 

7  // 
13 

86,412 

108,015 

151,221 

82,835 

110.447 

64,809 

86,412 

h" 

99,929 

124,911 

174,876 

94.248 

125, 664 

74,947 

99,929 

h" 

113,302 

141,628 

198,279 

106,397 

141,863 

84,977 

113,302 

h" 

127,405 

159,2.36 

222,959 

119,282 

159,043 

95,554 

127,405 

9    '/ 

IB 

142,205 

177.7.-.6 

248,859 

132,904 

177.20.", 

106,654 

142,205 

ft" 

157,659 

197,074 

1   275,903 

147,263 

196,350 

118,244 

157,659 

I" 

17"), 745 

219,681 

1   307,554 

162,356 

216,475 

131,809 

175,745 

1" 

192,678 

240,S48 

1   337,187 

178,187 

237,583 

144,509 

192,678 

111" 

1  [8 

212,620 

265.77.". 

I   372,085 

194,754 

259,672 

159,465 

212,620 

14' 

230,'J47 

288,684 

404,157 

212,057 

282,743 

173,210 

230,947 

i" 

Corners  of    J£J     nuts  =  1.414  flats. 

Thickness  of  nuts       =  diameter  of  bolt. 

Thickness  of  heads    =  flats  of  heads  and  nuts  -^  2. 

Sizes  of  "Sellers"  or  Franklin  Institute  finished  heads  and  nuts  are 
(flats  and  thickness  of  U.S.  rough  and  finished  nuts)  —  .0625".  Rough  heads, 
same  thickness  as  U.S.  nuts. 


338 


The  Naval  Constructor 


PROPORTIONS  OF  CLEATS 

(past.  Steel) 
Fig.  226. 

CAST   STEEL    CLEATS   SUITABLE   FOR    MANILA 

ROPE. 


Circumfer- 
ence 
of  Manila 
Rope. 

Corre- 
sponding 
Length  of 
Cleat. 
(Unit.) 

Weight 

in 
Pounds. 

Circumfer- 
ence 

of  Manila 
Rope. 

Corre- 
sponding 
Length  of 
Cleat. 
(Unit.) 

Weight 

in 
Pounds. 

In. 
1 

H 

2 

In. 
6 

8 

10 

12 

Lbs. 
2 

3 

6 

9 

In. 
3 

4 

In. 
14 

16 

18 

20 

Lbs. 
12 

17 

22 

31 

Proportions  of  Crane   Hooks 


339 


TABLE    OF  DIMENSIONS. 


r 

i. 


Fig.  227. 


Working 

A  — 

5  = 

c  = 

U  = 

E~ 

.Prr 

<?  = 

#= 

J= 

ix  Tons. 

1.00. 

1.00. 
Iu. 

1.80. 

.80. 

.40. 

1.00. 
In. 

3.00. 
In. 

1.60 

1.40 

III. 

Iu. 

Iu. 

In. 

In. 

In. 

i 

1 

f 

1J 

J 

i 

f 

H 

1 

I 

i 

i 

I 

1| 

f 

5 

1 

4 

21 

H 

n 

l 

\ 

I 

1    • 

1 1 

l  6 

i 

5 

2-? 

H 

i} 

H 

1 

1 

111 

1  3 
1^ 

TV 

1 

3 

If 

irV 

2 

n 

1* 

2 

I 

1  6 

H 

3| 

ltf 

irV 

3 

if 

If 

2* 

l| 

9 
To 

if 

n 

2* 

H$ 

5 

if 

If 

91  5 

1A 

1 

if 

■*; 

2T9* 

2i 

7 

2i 

s*i 

3H 

if 

I 

2* 

*'•; 

3f* 

3 

10 

-; 

- 

** 

ij 

M 

L'; 

n 

3f| 

3$ 

12 

-':■ 

~: 

H 

2| 

Mr 

-'; 

7* 

H 

3f 

15 

3 

3 

*ft 

2^ 

1* 

3 

9 

*tt 

4* 

18 

^i 

8* 

5* 

2f 

*A 

H 

9f 

6* 

4* 

21 

;;i 

8* 

2H 

i| 

31 

10  A 

5rV 

4 1 

25 

si 

Sf 

■'',■ 

3 

U 

sj 

"i 

6 

•I 

340 


The   Naval  Constructor 


CATTING  HOOKS  FOR  ANCHOR  FALLS 


Fig.  228. 


Weights  of  Boats  and  Davit   Diameters    341 


WEIGHTS     OF    BOATS    AND    DAVIT    DIAMETERS. 


Diameter  = 


Dimensions 

•A 

<  - 

—    X 

-  z 

of  Boats. 

ss* 

~-~< 

r  * 

Build 

r  3  ~ 

-  > 

§5 

of 
Boat. 

Description. 

L. 

B. 

D. 

~ 

<Z 

~C 

.. 

i   a 

i   a 

i  a 

a 

10 

4    3 

1    7 

670 

3  2 

2h 

Wood  clench 

Dinghy. 

12 

4    6 

1    9 

900 

3  4 

2| 

ti 

II 

ii 

14 

4    8 

1  11 

1,120 

3  6 

3 

u 

li 

ii 

16 

4  10 

2    0 

1,350 

3  8 

3i 

II 

li 

ii 

18 

5    0 

2    0| 

1.550 

3  9 

3i 

(( 

K 

Cutter. 

20 

5    4 

2    2" 

1,800 

4  0 

4 

[C 

li 

ii 

20 

5  10 

2    4 

2,000 

4  4 

4i 

it 

carvel 

Yacht's  launch. 

22 

5  10 

2    4 

2,240 

4  4 

4* 

(C 

clench 

Cutter. 

22 

6    0 

2    4 

2.450 

4  6 

4A 

(( 

curve] 

Yacht's  launch. 

24 

7    3 

3   0 

2,450 

5  5 

4* 

IC 

clench 

Lifeboat. 

24 

6    0 

2    9 

2,800 

4  6 

4| 

(( 

carvel 

Yacht's  launch. 

26 

7    6 

3    3 

2,700 

5  7 

5i 

ii 

clench 

Lifeboat. 

27 

5    9 

3   0 

5,600 

4  4 

5| 

(1 

diagonal 

Steam  pinnace. 

28 

8    6 

3    8 

2,900 

6  4 

5i 

u 

clench 

Lifeboat. 

30 

8    6 

3    8 

3,000 

6  4 

6 

li 

it 

Lifeboat. 

30 

7    0 

3  10 

7,600 

5  3 

71 

H 

diagonal 

Steam  navy  pinnace. 

32 

7    4 

4    0 

7,850 

5  6 

T| 

it 

ii 

ii          ii            ti 

36 

8    0 

4    3 

13.500 

6  0 

9 

ti 

n 

ti          it            ii 

40 

8    6 

4    9 

18.500 

64 

8    (3) 

K 

ii 

ii          it            ii 

42 

8    2 

4    6 

14,000 

62 

71  (3) 

l< 

it 

Royal  barge. 

45 

8    6 

4    6 

21.300 

64 

8f  (3) 

li 

ii 

Steam  navy  pinnace. 

47 

9    0 

4    6 

■J-_\-HNI 

6  9 

9    (3) 

II 

If 

it          it  "        it 

50 

9    3 

5    8 

23,500 

7  0 

Crane 

ti 

ii 

ii                        11                            >i 

56 

9    9 

4  10 

27,500 

7  4 

Crane 

u 

II 

li                       il                            11 

60 

9    6 

4  10 

•_>.r,uu 

7  2 

Crane 

it 

II 

11                       il                            11 

These  davit  diameters  are  figured  for  the  moment  exerted  with  the  ship 
inclined,  and  are  taken  for  a  fibre  stress  of  12,000  lbs.  per  square  inch,  with 
one  davit  taking  the  entire  load. 


342 


The   Naval   Constructor 


NAVY    STANDARD. 


Hinged  Watertight  Doors. 


Size  of  Opening  in 
the  Clear. 

Dimensions  over 
Door  Frame. 

Breadth  of 
Frame. 

i   n       i   a 

i     a        i    a 

5  6x30 

6,1}  x  3  7 

5  6x22 

6  1|  x  2  9 

5  0x30 

5  7}  X  3  7 

2>\  inches  each 
side  and  end  with 

5  0x20 

5  7f  X  2  7 

I   inch   extra  on 

4  0x20 

4  7|  x  2  7 

one  side  for  hinge 
pads. 

3  6x20 

4  If  x  2  7 

2  6x16 

3  1}  X  2  1 

Sliding  Watertight  Doors. 


/     //          /     // 

i     a        in 

4  9x20 

5  6£  x  2  8 

4"  V.S.W.T.D. 

3  3x20 

4  0£  x  2  8 

4"  V.S.W.T.D. 

Sliding   Watertight   Doors 


US 


SLIDING    WATERTIGHT    DOOR. 


[C 

I 
I 


I 

j 


ITT 


TT 


WROT.IRON    FACING    BARS 


--JU.1L 


o     o    o     o    /^  ~t\    o     o     5     o 


r 


SECTION  AT  A.B. 


i 


Fig.  229. 


3-U 


The  Naval   Constructor 

HINGED    WATERTIGHT   DOOR. 


® 


©         © 


@ 


®S 


@ 


g§) 


0 


© 

ft 


Fig.  230. 


Details   of  W.   T.    Doors 


345 


;5^i 


f — FT 


->. — 


CM 

I 
■ 

I 

V 


If 

-l3/4. 


'A 


Door  Plate/  ^ 


3~i 


II 

2yA  </♦  Rubber  ^f^ 
y<   Buttsn  Hd    Screws 

7/8   X    3/16   Strips 


I 


:. 


P2£§ 


ft   " 


'IT 


'/*l 


^        '     :-r-+1-C8-0' 


St 


4'/«  x  iy8  x  %o 


J 


£.  ]   Bulkhd.  Plating 

Standard  Gas 
Pipe  Threads 


DETAIL  OF   DOGS 
Fig.  231. 


" 


7/g  Hinge  Pm 


■  „  , 


3/4  Rivets  ' 


■* 2"/"6 4m'/"-^| 


V4  Rivets 


, 


-2'/2  x  V*  Rubber 


<-1'/4  ^ 


\    Buikhd. Plating 


DETAIL  OF   HINGES 
Fig.  232. 


346 


The   Naval   Constructor 


STANDARD    EYEBOLTS. 


B. 


C. 


D. 


E. 


G. 


Breaks 

at 

Toxs. 


1 

4 


A 


25 
32 


II 
16 


_5 
32 


15 
32 


_3_ 
16 


If 


3 

8 


7 
T6 


9 

32 


64 


1* 


1JL 

132 


3 

16 


1  3 
64" 


II 

16 


25 
3  2 


i 


_9_ 
3  2 


21 


o 
O 


1 

2 


1 

n 

u 


13- 


3 


15 
3  2" 


9 

T6" 


3 
I 


1  3 

1? 


7 


if 


1  3 
1  5 


111 

2* 


9  l 


9  3 


Q  1 


3  5 


1A 

x16 


1  3 

1  8 


11 


113 

x16 

2 


O  7 


2f 
81 


32 


1 

1~ 


5 
T6~ 


11 

32 


15 
32 


9 
T6~ 


3 


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1A 

x16 

n 


9  3 


2h 


21 


5 

16 


7 
T6 


9 

T5 


5 

5 


II 

16 


3 
I 


13 
16 


5 

6 

8 

22 


27 


33 
40 

47 
50 


Table   ot   Fairleads 


347 


TABLE    OF   FAIRLEADS  (Cast  Iron). 
Single  Roller. 


-+-25 


r--Hn--4*: — 1-25 4 


Fig.  234. 


Length 

of 

Ship  (Ft.). 

Uxit 

DIMEN- 
SION  IX 

INCHES. 
d. 

Approxi- 
mate 
Weight  ix 
Pounds. 

Length 

OF 

Ship  (Ft.). 

Uxit  Di- 

MEXSIOX 

IX 
IXiRES. 

d. 

Approxi- 
mate 
Weight  ix 
Pounds. 

100 

3 

34 

470 

11 

1,670 

110 

H 

54 

490 

iii 

1,907 

120 

4 

80 

520 

12 

2,167 

150 

4} 

115 

550 

m 

2,450 

170 

5 

156 

570 

13 

2,750 

190 

5* 

208 

600 

m 

3,085 

200 

•6 

271 

620 

14 

3,435 

215 

6* 

345 

650 

m 

3,820 

240 

7 

430 

680 

15 

4,230 

280 

7^ 

530 

710 

15* 

4,670 

300 

8 

644 

740 

16 

5,140 

330 

8* 

770 

760 

m 

5,635 

360 

9 

915 

780 

17 

6,165 

390 

9* 

1,073 

800 

17) 

6,720 

410 

10 

1.253 

850 

18 

7,315 

440 

10) 

1,452 

•      •      •      ■ 

.... 

Weight  -without  roller     =  d3  x  .6  =  lbs. 
Weight  with  one  roller    =  d3  x  1.25. 
Weight  with  two  rollers  =  d 3  x  1-5. 


348 


The  Naval  Constructor 


STANDARD   FLANGES    FOR    LEAD    PIPES. 


Bolt  Holes  Drille. 


note:   no  finish  on  cast  iron  flanges 
Fig.  235. 


From  0  to  100  Pounds  Pke 

iSURE 

• 

> 

"3  . 

-5! 

u 

a; 

-*a 
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0^  ao 

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B. 

c. 

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G. 

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L. 

if. 

tf. 

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8 

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1 
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8 

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4 

1 
4 

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5 

5 

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3 
4 

6 

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111 

9* 

7 

if 

151 

13* 

1 

i 

5 
T6 

10 

7 

3 
4" 

Standard    Pipe    Flanges 


349 


PIPE    FLANGES,   STANDARD. 


Fig.  236. 


Fr<>m  0 

to  100  Pounds  Pressure  per  Squ 

are  Inch. 

-**  ~  7* 
£.7.'~ 

£ 

—  — 

Z  '- 

—  - 

—  n 

—  s 
-.  a 

.z  — 

■— 

z 
■-  ■• 

-  c 

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—    — 

0 

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23 

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*—     — 

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— < 

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r. 

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0 

PQ 

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u 

30  - 

43 

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-*.    .* 

— 

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— 

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£. 

c. 

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G. 

0. 

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a 

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6 

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6.625 

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01 

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5 

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8 

/ 

350 


The   Naval   Constructor 


STANDARD   FLANGES   FOR   VENTILATION. 


t^—^A — -a 


Figs.  237  to  239. 


A. 


Inside 

Diameter 

of 


Pipe. 


21 
2| 
3 

31 
4 

41 
5 

5* 
6 

6* 
7 

7* 
8 


Flange 


2| 

2f 
2| 
3i 
3f 

5k 


6i 


7* 
7f 
81 


Bolts. 


No. 


10 


Size 


3 

3 

4 

3 

8 

4 

3 

8 

4 

3 

8 

5 

3 

8 

5 

3 

8 

6 

3 

8 

7 

3 

8 

7 

3 

8 

8 

3 

8 

8 

3 

8 

9 

3 

8 

9 

3 

8 

Inside 

Diameter 

of 


Pipe. 


8J 

9 

91 
10 
101 
11 

Hi 

12 

12* 

13" 

131 

14" 

141 

15 

151 

16 


Flange 


8| 

91 

9f 

101 

10| 

111 
llf 

121 
12| 
131 
13f 
141 
14| 
151 
15f 
161 


Bolts. 


No. 


8 

8 

9 

9 

9 

10 

10 

11 

11 

11 

12 

12 

12 

13 

13 

14 


Size. 


i 
i 

2 
1 

i 

i 

2" 
1 


1 
Z 
1 

1 


I 

2" 


c. 


Inside 

Diameter 

of 


Pipe. 


17 

171 

18 

181 

19 

191 

20 

201 

21 

211 

22 

221 

23 

231 

24 


Flange. 


1  9 

17f 

181 
18| 
191 
19f 
201 
20f 
211 
21f 
221 
22| 
231 
23 


Bolts. 


No. 


11 
12 
12 
12 
13 
13 
13 
14 
14 
14 
14 
15 
15 
15 
16 
16 


Size. 


i 


Hand  Wheels 


351 


HAND    -WHEELS    (Iron). 


Fig. 

240. 

Diameter. 

No. 

OF 

Arms. 

A. 

B. 

C. 

J). 

#. 

F. 

e. 

H. 

K. 

a 

ft 

u 

tt 

a 

a 

a 

tt 

a 

2 

\ 

K 

9 

3 

TS 

1 

4 

5 
T6 

\ 

tV 

4 

24 

7 
1  6 

a 

4 

3 

1  •> 

1 

1 

5 

1  6 

i 

4 

3 

4 

7 

J 

5 

TS 

7 
T7 

f 

A 

4 

34 

t 

1 

1 

5 

T6 

4 

tV 

4 

4 

4 

1  1 

TS 

1    \ 

1? 

I 

9 

4 

5 

44 

a 

"     1 

s 

1  6 

A 

1 

4 

9 

5 

5 

14 

1  6 

ItV 

1 

7 
T7 

1 1 

4 

1 

5 

6 

7 

8 

1| 

1 

4 

1 

9 
TS 

1 1 

TS 

6 

i 

1 

n 

7 
T5 

4 

I 

i 

1 

6 

8 

ItV 

m 

7 

4 

.tt 

l  l 

1  3 

TS 

6 

0 

n 

i« 

4 

9 

1 

1 

7 

s 

6 

10 

i 

1 1 

4 

1 

ItV 

1  3 

TS 

• 

6 

12 

ItV 

2T 

9 

T* 

1  1 

ItV 

7 

9 

ItV 

6 

14 

1* 

9   9 

^TS 

* 

If 

1 

ItV 

6 

16 

i  s 

1  1 

if 

ItV 

1   1 

1  , 

6 

18 

1 1 

31 

I 

5 

1   \ 

1  J 

6 

21 

1 

••:• 

R 

1 

If 

1    ■ 

If 

6 

24 

2* 

4 

7 

IrV 

li 

14 

1* 

6 

352 


The  Naval  Constructor 


HAND    WHEELS    (Brass). 


Fig.  241. 


DlAM., 

A. 

B. 

C. 

D. 

E. 

G. 

H. 

7T. 

XO.   OF 

Arms. 

ti 

// 

a 

a 

a 

a 

a 

a 

a 

n 

5 
16 

9 

16 

l 

8 

l 

I 

3 

1  6 

i 

4 

4 

2 

3 

§ 

1 

l 

1 

5 

4 

8 

8 

8 

4 

4 

1  6 

H 

< 
1  6 

3 
4 

1 

8 

5 
1  6 

5 
1  6 

3 

8 

4 

3 

7 
16 

7 
8 

1 

8 

5 

16 

5 
16 

7 
1  6 

4 

3| 

1 

2 

H 

3 

1  6 

3 

8 

2. 

8 

* 

4 

4 

1 

2 

ifV 

3 

1  6 

3 
8 

3 

8 

9 

4 

*1 

9 

H 

3 

7 

7 

5 

4 

1  6 

1  6 

16 

1  6" 

8 

5 

5 

8 

H 

3 

16 

1 
2 

7 
16 

5 
5 

4 

6 

1  1 
1  6 

if 

1 
4 

9 

1  6 

1 

2 

1  1 
16 

4 

7 

3 
4 

if 

1 

4 

5 

8 

9 
16 

3 

4 

4 

8 

7 
8 

U 

5 
1  6 

1  1 
16 

5 

8 

1  3 
16 

4 

9 

1  5 

1  6 

2 

5 

16 

3 
4 

5 

8 

7 
7? 

4 

10 

2 

3 

8 

1  3 
1  6 

1  1 
1  6 

1  5 
16 

5 

11 

1    1 

xl  6 

2* 

3 
f 

i 

8 

3 
4 

1 

5 

12 

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n 

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15 
16 

3 
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7 
8 

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5 

16 

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xl  6 

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1  5 
1  6 

1A 

6 

18 

1    5 
x   8 

^tV 

9 

16 

11 

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lf6 

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21 

1    7 

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l  a 

1    8 

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1    & 

1   8 

6 

24 

2TV 

31 

1  1 
16 

111 
x16 

1A 

1   2 
4 

6 

Keys  and    Keyvvays. 


353 


KEYS    AND    KEYWAYS. 

D  =  diameter  of  .shaft  in  inches.  -4 — 

W  =  width  oi  key  and  keyway  in  inches, 

T  -  thickness  of  key  =  &  D  +  |". 
Taper  =  J"  per  foot. 

t  —  depth  in  shaft  \  measured  at  the 
T  —  t  =  depth  in  hub    )      side. 


Fig.  242. 


* 

jr. 

T. 

t. 

7'—  «. 

D. 

FT. 

T. 

t. 

T—t. 

II 

// 

a 

II 

a 

a 

a 

a 

a 

ft 

1 

3 

32" 

3 

1  0 

1 

1  6 

l 

s 

5 

1:' 

5 

8 

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4 

■ 

1 

1 
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1  6 

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1  6 

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54 

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8 

2 

4 

1 

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9 

3 
16 

1 

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8 

1 
4 

f 

7 
8 

9 
32 

7 
32 

3 
3"2" 

i 

6* 

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1  1 

16 

5 
1  6 

t 

1 

5 
1^ 

7 
3? 

3 

32 

4 

6 

14 

1  1 
1  6 

5 

TO" 

i 

n 

1  1 

3  2 

1 
4 

3 

3  2 

5 
32" 

64 

1A 

3. 
4 

5 
1  6 

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16 

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3 

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6$ 

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32 

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If 

1 
4 

5 
1  6 

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1  3 

3  2 

1 

3 

32 

5 

32 

7 

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1  6 

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5 
1  6 

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3 

1  6 

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_7 
To 

f 

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4 

5 

To 

10$ 

24 

14 

8 

1 

354 


The   Naval   Constructor 


HAWSE  PIPE  PROPORTIONS 

(SEE  TABLE  OF  WEIGHT8) 


CHAIN  CABLE  =  UNIT. 


FiO.  243. 


-4  =  9.0,  B=.6,   C  =  .7,  £-=.5,  £=3.6,  F=5.0,   G  =  4.7. 


Hawse   Pipe   Weights 


355 


HAWSE    PIPE    WEIGHT    FOR    STOCKLESS 

ANCHORS. 

Including  Pipe,  f.ij>s,  find  Deck  Ring.) 


Cable 

Weight  of 

Cable 

• 

Weight  of 

(^Stud  Link). 

Hawse  Pipe. 

(St id  Lixk). 

Hawse  Pipe. 

Ius. 

Lbs. 

Ins. 

Lbs. 

1 

1,000 

2T% 

4,400 

hh 

1.030 

2f 

4,700 

n 

1,060 

h\ 

5,100 

ia 

1.100 

2§ 

5,500 

i* 

1,200 

2A 

6,000 

M  6 

1,300 

2| 

6,500 

!| 

1,400 

»H 

7,100 

h\ 

1,500 

2| 

7,700 

1* 

1,560 

Ol  3 

8,500 

h% 

1,700 

9  1 

9,300 

If 

1,800 

Ol  5 

ZT6 

10,200 

m 

2,000 

3 

11,400 

if 

2,100 

«A 

12,750 

HI 

2,300 

3* 

14,000 

U 

2,500 

3fV 

15,500 

in 

2,700 

3* 

16,500 

2 

3,000 

3TV 

18.000 

2A 

3,200 

3| 

19,500 

2i 

3.400 

3TV 

21,000 

2^ 

:j.750 

3} 

22,500 

n 

4,000 

.    .   . 

•       ■       •       • 

N.B.  —  Weights  given  are  for  one  pipe. 


356 


The   Naval   Constructor 


B-  2 

Ho 


h-1 


»/•*  r**i  ,— i  i  ^  nn  —  rr\  \  —  r/i  rvi  rr\  ■  _  -*.   -v^  r— *  r^* 


T-IMrH  jl^M 


02 
H 
J 

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364 


The   Naval   Constructor 


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366 


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Fig.  253. 


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The   Naval   Constructor 


TOWING   BITTS.     (Cast  Iron.) 

5.1-1— 


*r   .0555 

Av-  -  -  =n 


-*  w_1..166->| 

1  * r  w^r*4 


Diameter. 

"Weight 

of 
Casting. 

"Weight  of 

Fastenings  and 

Chock. 

Total  Weight. 

In. 

Lbs. 

Lbs. 

Lbs. 

12 

2,040 

145 

2,185 

15 

3,975 

280 

4,255 

18 

6,875 

480 

7,355 

21 

10,900 

765 

11,665 

24 

16,500 

1,140 

17,640 

Weights  of  Brass   Framed  Sidelights      369 


WEIGHTS    OF    BRASS    FRAMED    SIDELIGHTS. 


Diameter 
(Clear  Glass). 

Dbs<  KIPTION". 

Bkass. 

Gla--. 

Total. 

Iu. 

Lbs. 

Lbs. 

Lbs. 

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To  open.     No  deadlight 

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370 


The   Naval   Constructor 


PROPORTIONS    OF    CHAIN   SLIPS. 


Fig.  256. 


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372 


The  Naval   Constructor 


THIMBLES    FOR    WIRE   ROPE. 


t---§--H 


(BULLIVANTS.) 


Wire  Rope. 

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Toggle    Pins 


373 


TOGGLE   PINS     (STANDARD). 


Fig.  259 


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374 


The   Naval   Constructor 


Fig.  260. 


Admiralty   Turnbuckles 


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ADMIRALTY    TURNBUCKLES,    ETC. 
Steel  Wire  Rigging. 


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The  Naval  Constructor 


WEIGHT    OP   STANDARD    VENTILATOR    COWLS. 

(See  Fig.  261.) 


Diameter 

of 

Ventilator 

Trunk. 

Length  of 

Parallel 

Neck  below 

Centre 

of  Throat 

Radius. 

Area  in 

Square 

Feet  Plus 

Laps. 

Weight 
of  Cowl  in 

Pounds, 
Exclusive 

OF 

Fittings. 

Thickness 

in 
U.S.  Gauge. 

In. 

In. 

Sq.  Ft. 

Lbs. 

10 

H 

5.5 

11.25 

No.  18  U.S.  G. 

12 

3 

7.5 

15.50 

14 

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10.5 

21.50 

16 

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13.75 

28.00 

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H 

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35.75 

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45.00 

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27.00 

55.00 

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6 

32.50 

66.25 

26 

6| 

39.00 

79.50 

28 

7 

45.50 

93.00 

30 

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53.75 

172.00 

No.  14 

33 

81 

64.50 

205.00 

36 

9 

77.50 

247.00 

42 

10J 

105.00 

335.00 

48 

12 

135.00 

430.00 

Standard   Ventilating   Cowls  3  i  7 


STANDARD    VENTILATING    COWLS. 


^ 

iv 

Proportions. 

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11 

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II 

F  =    .216. 

l.JL 

G=    .375. 

H-    .75. 

k 

IT        _^ 

1 

p 

A 

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Fig. 

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Section  IV. 

RIGGING  AND   ROPES. 


CHAPTER    I. 

The  rigging  and  ropes  of  a  modern  steamship  still  constitute  a 
very  important  part  of  the  vessel's  equipment,  notwithstanding 
the  almost  total  abolition  of  sail  area,  and  its  extinction  as  a 
propelling  agent  in  the  present  day  steamer. 

Generally  too  little  attention  is  devoted  to  what  are  considered 
the  minor  details  of  a  steamship's  rigging,  by  those  best  qualified 
to  determine  the  sizes  of  ropes  and  blocks,  and  the  arrangement 
of  tackles  on  a  mechanical  basis.  The  array  of  derricks  around 
the  masts  and  kingposts  of  a  freighter,  with  their  varying  loads  of 
from  2 £  to  50  tons,  exemplify  the  necessity  for  a  closer  acquaintance 
with  the  staying,  guying  and  tackling  of  these  appliances,  to  en- 
sure that  the  whole  of  the  system  shall  be  designed  throughout  on 
an  uniform  basis. 

RIGGING. 

By  theterm  "rigging"  is  generally  denoted  the  standing  rigging, 
or  that  part  whose  function  is  to  stay  or  support  the  masts,  spars 
and  funnels,  and  comprises  the  shrouds,  guys,  pendants,  bowsprit 
shrouds,  jib-boom  guys,  stays  and  backstays.  These  supports  are 
now  invariably  made  of  galvanized  wire  rope,  either  iron  or  mild 
steel,  the  latter  being  employed  where  strength  and  lightness  are 
desired,  or  where  heavy  working  derricks  are  fitted.  A  special 
quality  called  plough  steel,  is  sometimes  used  when  exceptionally 
great  loads  have  to  be  lifted.  Indeed,  it  will  often  be  found 
cheaper  to  employ  plough  steel  in  these  cases,  as  the  number  of 
shrouds  or  stays  may  thereby  be  reduced,  thus  effecting  a  greater 
saving  in  the  quantity  required  than  the  extra  cost  in  quality  has 
involved. 

Wire  Rope.  —  As  its  name  implies,  wrire  rope  is  manufactured 
from  small  steel  or  iron  wires,  twisted  into  strands,  six  of  which 
(usually)  are  laid  up  around  a  tarred  hemp  centre,  the  strands 
having  a  wire  heart  where  strength  is  more  important  than  flexi- 

•°.79 


380  The  Naval  Constructor 


bility,  otherwise  where  used  as  running  gear  and  flexibility  is  a 
necessity  they  also  have  a  hempen  centre.  The  number  of  wires 
constituting  a  strand  varies  with  the  degree  of  flexibility  required, 
19  wires  to  a  strand  being  ordinary  flexible  rope,  and  37  wires 
extra  flexible,  such  as  would  be  used  for  derrick  topping  lifts. 
Steel  wire  rope  for  ship  rigging  should  always  be  galvanized, 
otherwise  it  deteriorates  rapidly,  and  where  it  is  used  for  running 
gear,  it  should  be  soaked  in  boiling  tallow  and  linseed  oil,  a 
process  which  will  add  much  to  its  life. 

Great  care  must  be  used  at  all  times  in  handling  it  so  as  to  avoid 
sharp  nips  or  kinks,  either  of  which  is  fatal.  For  this  reason 
when  used  as  hawsers,  wire  rope  must  be  stowed  on  a  reel  having 
a  core  of  suitable  diameter,  and  in  the  case  of  running  rigging,  the 
proper  diameter  of  sheave  for  a  given  size  of  wire  is  important. 
An  undersized  sheave  shortens  the  life  of  the  best  rope,  and  by 
distorting  the  fibres,  weakens  its  strength. 

Approximate  diameters  of  sheaves  for  extra  flexible  steel  wire 
rope,  are  given  in  the  table  on  page  381. 

Splices.  —  Splices  in  wire  rope,  such  as  are  necessary  around 
thimbles  and  elsewhere,  weaken  its  strength  from  10  to  15  percent. 
It  is  necessary,  therefore,  to  take  account  of  this  in  fixing  on  the 
safe  working  load.  Likewise  in  ordering  the  lengths  of  rope, 
allowance  must  be  made  on  net  sizes  for  the  number  of  splices 
worked. 

Thimbles.  —  In  working  eyes  in  the  ends  of  wire  rope,  it  is 
necessary  that  the  fibres  forming  the  inside  of  eye  should  be 
protected  from  the  destructive  effect  of  a  link  or  shackle  pin 
bearing  on  same.  To  guard  against  this,  the  splice  is  worked 
around  heart  shaped  eyes  or  thimbles.  These,  like  the  sheaves, 
must  be  of  a  suitable  size  for  a  given  circumference  of  rope. 


Sheaves  and  Splices 


381 


SHEAVES    FOR    EXTRA    FLEXIBLE    STEEL 

WIRE  ROPE. 

For  Steering  Leads,  Topping  Lifts  and  Purchases. 


ClBCUM- 

DIAMETER 

Weight 

( JlBCUH- 

Diameter 

WEIGHT 

FEREN<  1". 

OF 

IN 

FEBENCE 

of 

IN 

of  Rope. 

Sheave. 

Brass.* 

OF  Hope. 

SHEAVE. 

Brass* 

In. 

In. 

Lbs. 

.  In. 

In. 

Lbs. 

1 

U 

•_". 

»\ 

16 

40 

14, 

6 

o\ 

'J4 

17 

54 

if 

7 

8h 

4 

18 

66 

8 

11 

■ii 

19 

78 

2 

9 

15 

4i 

20^ 

107 

H 

10i 

20 

4f 

21* 

120 

2h 

12 

26 

5 

23 

138 

2| 

3 

13 

29 

5* 

25 

163 

14 

34 

6 

27 

190 

H 

W 

37 

6i 

30 

235 

*  Weight  in  cast  iron  =  Brass  X  .85. 


LENGTH  OF  WIRE  ROPE  REQUIRED  FOR 

SPLICES. 


ClBCUM- 

ALLhWANi  I 

Allow  ote 

ferf.N't:  of 

for  Ikon  Wire 

for  Steel  Wire 

Manila. 

Rope. 

Rope. 

Rope. 

In. 

In. 

In. 

1 

'.» 

VI 

l* 

12 

18 

2 

1.-. 

21 

2.1 

is 

24 

An     average 

3 

20 

30 

allowance  of  1 5 

3$ 

22 

33 

inches  is  made 

4 

24 

36 

for  Manila. 

41 

27 

30 

5 

30 

42 

6 

35 

18 

7 

40 

:,4 

382 


The  Naval   Constructor 


GALVANIZED    IRON    AND    STEEL    WIRE 
RIGGING   ROPES. 


To  Admiralty  or  Lloyd's  Kequirements. 


Sizes. 

Breaking  Stress. 

Weight 
per 

Best  Best 

Galvan- 

Galvanized 

Circum. 

Diameter. 

Fathom. 

Galvanized 

ized  Mild 

Patent 

Iron. 

Steel. 

Steel. 

Inches. 

Indies. 

Lbs. 

Tons. 

Tons. 

Tons. 

1 

.318 

0.96 

1.2 

1.75 

2.8 

H 

.397 

1.2 

1.5 

2.25 

3.6 

n 

.397 

1.5 

1.87 

3 

4.5 

if 

.437 

1.8 

2.25 

3.25 

5.4 

n 

.477 

2.1 

2.62 

4 

6.3 

if 

.517 

2.5 

3.12 

5 

7.5 

if 

.557 

2.9 

3.62 

5.5 

8.7 

8 

.596 

3.3 

4.12 

6 

9.9 

2 

.636 

3.8 

4.7 

7 

11.4 

2J 

.676 

4.3 

5.3 

8 

12.9 

n 

.716 

4.8 

6.0 

9 

14.4 

n 

.755 

5.3 

6.6 

10 

15.9 

n 

.795 

5.9 

7.3 

11 

17.7 

2f 

.835 

6.6 

8.2 

12 

19.8 

2f 

.875 

7.1 

8.8 

13 

21.3 

2f 

.915 

7.8 

9.7 

14.5 

23.4 

3 

.954 

8.5 

10.6 

,  16 

25.5 

3| 

.994 

9.2 

11.5 

17.5 

27.6 

3| 

1.03 

9.9 

12.3 

19 

29.7 

3| 

1.07 

10.7 

13.3 

20.5 

32.1 

3i 

1.11 

11.5 

14.3 

22 

34.5 

3| 

1.15 

12.3 

15.3 

24 

36.9 

3f 

1.19 

13.2 

16.5 

26 

39.6 

y7 
"8 

1.23 

14.1 

17  6 

28 

42.3 

4 

1.27 

15,0 

18.7 

30 

45.0 

4| 

1.31 

16.0 

20.0 

32 

48.0 

4i 

1.35 

17.0 

21.2 

34 

51.0 

43 

^8 

1.39 

18.0 

22.5 

36 

54.0 

41 

1.43 

19.0 

23.7 

38 

57.0 

4f  • 

1.47 

20.1 

25.1 

40 

63.3 

4f 

1.51 

21.2 

26.5 

42 

63.6 

47 

8 

1.55 

22.4 

28.0 

44 

67.2 

5 

1.59 

23.5 

29.3 

48 

70.5 

5i 

1.67 

26.0 

32.5 

53 

78.0 

5i 

1.75 

28.5 

35.6 

58 

85.5 

6" 

1.9 

34.0 

42.5 

68 

102.0 

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384 


The  Naval  Constructor 


TABLE   OF   MILD    STEEL   OPEN   THIMBLES. 


For  Steel  Wire  Rope  or  Hawsers. 

(British  Admiralty.) 


Circum- 
ference 

of 
Rope  or 
Hawser. 

Score. 

Size  i> 

r  Clear. 

Weight 
Each. 

Width. 

Depth. 

Width. 

Length. 

In. 

In. 

In. 

In. 

In. 

Lbs. 

1 

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.87 

1.50 

i 

n&n 

.6 

o 
.o 

1.31 

2.25 

9 
T6 

lf&2 

.8 

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1.75 

3.00 

1    1 

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1.0 

.5 

2.18 

3.75 

9  fi 

2f  &3 

1.2 

.6 

2.62 

4.50 

314 

3* 

1.4 

.  t 

3.06 

5.25 

6 

4 

1.6 

.8 

3.50 

6.00 

9 

41 

1.8 

.9 

3.93 

6.75 

HJ 

5 

2.0 

1.0 

4.37 

7.50 

16  \ 

5| 

2.2 

1.1 

4.81 

8.25 

23  \ 

6 

2.4 

1.2 

5.25 

9.00 

26  | 

«1 

2.6 

1.3 

5.68 

9.75 

37  J 

7 

2.8 

1.4 

6.12 

10.50 

44  \ 

8 

3.2 

1.6 

7.00 

12.00 

66  i 

Wrought  and   Cast   Iron   Thimbles      385 


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380 


The   Naval   Constructor 


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Wire   Rope   End-Fittings 
WIRE    ROPE    END-FITTINGS. 


o87 


.SHOE  WJTH  RIVETS. 


thimble.  mo  hook  . 
Figs.  264-271. 


388  The   Naval   Constructor 


Rope  End  Fittings.  —  Another  method  of  forming  an  eye  on 
the  end  of  wire  rope,  is  to  work  an  open  eye  with  groove-shaped 
ends,  to  enclose  the  rope,  and  through  which  they  are  riveted  as 
shown  in  the  plate.  This  "  shoe,"  however,  is  rarely  resorted  to 
unless  on  the  bowsprit  shrouds,  and  similar  rigging  on  yachts, 
where  small  close-fitting  eyes  are  desired  for  neat  appearance. 

Some  of  the  more  common  forms  of  wire  rope  end  fittings  are 
illustrated  on  the  preceding  page.  Their  various  uses  will  suggest 
themselves  to  the  observant. 

Parcelling  and  Serving. —  In  ordinary  merchant  work,  the 
lower  ends  of  shrouds  and  stays  for  6  or  7  feet  are  wormed  and 
parcelled  with  two  overlapping  layers  of  cotton  sheeting,  painted 
and  thereafter  served.  Where  stays  are  subjected  to  much 
chafing,  they  should  be  doubly  served  and  covered  with  leather 
in  the  collars. 

No  serving  must  be  fitted  on  stays  which  carry  sails,  as  it  would 
only  be  cut  to  pieces  by  the  chafe  of  the  hanks. 

Turnbuckles.  —  Standing  rigging  is  invariably  set  up  with 
turnbuckles,  or  rigging  screws  to  enable  the  wire  to  be  tautened, 
as  quite  an  appreciable  amount  of  "stretch"  takes  place,  more 
particularly  in  new  rope. 

These  screws  are  proportioned  to  the  breaking  strength  of  the 
wire,  which  should  be  sjMced  around  a  solid  heart-shaped  core 
for  the  heavier  sizes,  or  an  open  thimble  in  the  case  of  light  wire. 
Where  used  for  shrouds,  the  lower  end  must  be  arranged  to  swivel 
freely,  and  the  pad-eye  riveted  to  sheerstrake,  the  connection 
developing  the  same  strength  as  the  screw.  Where,  however,  they 
are  set  up  fore  and  aft  on  stays,  the  pad  should  have  a  shackle-eye 
for  pin,  as  'thwartship  movement  is  not  then  desirable,  and  the 
shackle-eye  will  permit  of  a  smaller  diameter  pin  being  used. 

In  proportioning  screws  under  one  inch  in  diameter,  an  allow- 
ance of  about  20  per  cent  must  be  added  to  the  area  of  metal  at 
root  of  thread,  as  compensation  for  the  loss  of  strength  sustained 
in  cutting  the  screw.  Screws  should  be  smeared  with  tallow  and 
coated  with  a  canvas  cover. 

Sheerpoles.  —  It  is  usual  to  fit  a  rod  to  the  heads  of  turn- 
buckles to  shrouds  connecting  and  supporting  the  heads  in  their 
relative  position,  and  preventing  the  screws  from  slacking  back. 
In  small  vessels  it  may  be  from  §"  to  §"  diameter,  seized  to  each 
head  with  seizing  wire.  Where  heavy  rigging  is  dealt  with,  the 
sheerpole  is  bolted  through  the  heart  of  tumbuckle,  and  bosses 
jumped  on  to  form  receptacles  for  belay  pins. 

Ratlines  —  Are  commonly  made  of  hemp  or  wire  rope,  seized 
at  outer  shrouds  and  passing  around  the  others  in  a  clove  hitch, 


Ropes 


389 


and  spaced  about  24  inches  apart.     Rope,  however,  is  being  fast 
displaced  by  iron  rod  ratlines,  seize!  with  wire  to  shrouds. 

ROPES. 

Manila  and  hemp,  tarred  and  white,  are  the  materials  from 
which  most  ship's  ropes  are  made.  As  its  name  indicates, 
••Manila11  hails  from  the  Philippines,  and  is  made  from  the 
fibre  of  the  wild  banana.  Hemp  rope  is  made  from  the  fibre  of 
the  hemp  plant,  the  Russian  variety  being  most  generally  used. 
Tow  lines  are  sometimes  made  of  coir,  which  is  manufactured 
from  the  tough  fibrous  husk  of  the  cocoanut.  In  referring  to 
ropes,  the  circumference  always  denotes  the  size. 

Manila. — All  running  ropes  and  those  used  for  sundry  work 
on  shipboard  are  made  of  Manila,  as  hemp,  though  stronger 
when  white,  is  not  pliable  enough.  It  is  usual  to  make  it  of  3 
strands,  although  4-stranded  or  shroud-laid  rope  is  also  made ;  and 
for  yacht  work,  4-strand  Manila  is  best,  as  it  is  smaller  in 
diameter  for  a  given  strength,  besides  being  neater. 

Manila  is  of  greater  strength  than  tarred  hemp,  and  stands  the 
weather  much  better  than  the  untarred  or  white  hemp,  although 
not  so  strong  as  the  latter. 

The  following  tables  give  strengths  and  weights  of  Manila, 
hemp,  and  coir  ropes  :  — 


390 


The   Naval   Constructor 


MANILA    ROPE. 


Circum- 
ference 
of  Rope. 

Diam- 
eter 

of 
Rope. 

Wt. 

per 

Foot. 

Break- 
ing 
Stress. 

£  a  o 

-    —  -  - 

3£§ 

Diame- 
ter of 
Rope. 

Wt. 

PER 

Foot. 

Break- 
ing 
Stress. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

i 

2 

3 
16 

.035 

405 

4| 

14 

.640 

16,200 

3 
4 

1 

.045 

585 

5 

if 

.720 

20,000 

1 

5 

TS 

.055 

700 

5i 

if 

.835 

23,650 

H 

| 

.065 

900 

6 

1    2 

1   8 

1.05 

27,000 

H 

7 
16 

.075 

1,170 

H 

2 

1.15 

29,250 

H 

4 

.085 

1,800 

6i 

21 

1.25 

31,690 

if 

9 
16 

.110 

2,295 

1 

21 

1.42 

33,800 

2 

5 
f 

.140 

3,200 

74 

2| 

1.70 

36,750 

n 

3 
4 

.170 

3,750 

8 

2A 

2.00 

39,200 

n 

13 
16 

.200 

4,050 

84 

2| 

2.30 

50,000 

2f 

7 
8 

.240 

6,050 

9 

9  7 

Z  8 

2.65 

54,190 

3 

1 

.275 

7,200 

9i 

3 

3.00 

57,800 

3i 

It1* 

.325 

7,875 

10 

3A 

3.40 

75,000 

81 

11 

.360 

9,800 

11 

34 

4.00 

96,000 

3| 

1t36 

.410 

10,500 

12 

3| 

4.70 

101,000 

4 

11 

.460 

11,250 

13 

41 

5.65 

117,000 

41 

1  ? 

-1  8 

.510 

13,500 

14 

41 

6.50 

158,300 

4| 

116 

.585 

14,450 

15 

5* 

7.50 

172,500 

Hemp   Cordage 


391 


HEMP    CORDAGE. 


"  -  2 

a  s  - 

-  —  — 

— 

ft  ■/. 

1  ':• 
<  M 

■^--  ■ 

Kind. 

—  —  --* 

§    1 

^  - 

-*  T  — 

Sac 

t»t 

-  - 

tiOQ 

.~ 

— 

tH 

In. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

n 

h 

I 

1 

6 

.018 

336 

.015 

476 

12 

.037 

072 

.031 

1,008 

4o  Thread 

15 

.017 

896 

.039 

1,344 

Yarn  Hemp. 

n 

21 

.062 

1,120 

.052 

1.080  1 

33 

.098 

1,680 

.083 

2,352 

Tarred  is 

if 

42 

.125 

2,240 

.105 

3,136 

Riga. 

* 

2 

54 

.161 

3,024 

.134 

4,144 

24 

66 

.196 

3,808 

.160 

5.102 

White  is 

2< 

84 

.250 

4.48<) 

.208 

6,496 

Italian. 

•' 

102 

.302 

5,600 

.240 

7.800 

3 

120 

.355 

6,720 

.200 

9,408 

3i 

105 

.414 

7.-40 

.331 

11.000 

30  Thread 

4 

3\ 

123 

.485 

-.512 

.403 

12.544 

Yarn  Hemp. 

4" 

159 

.626 

11,200 

.522 

16,240 

„     Tarred  is 

41 

201 

.791 

14.448 

.001 

20.72H 

Riga. 

5 

249 

.995 

17.696 

.816 

25,760 

White  is 

6 

360 

1.40 

25,760 

1.18 

30.901) 

Italian. 

6J 

351 

1.66 

28,672 

1.40 

43,200 

;       25  Thread 

7" 

4i  »s 

1.92 

33,152 

1.01 

47.0'  hi 

Yarn  Heini>. 

71 

468 

2.07 

38,000 

1.85 

51,520 

Tarred  is  St. 

8" 

534 

2.52 

4:5.456 

2.11 

58.210 

Petersburg. 

9 

675 

3. 18 

53,760 

2.o<; 

73.!  120 

White  is 

12 

1,200 

5.65 

96,500 

4.72 

131,040 

Italian. 
j 

Hemp. — Hemp  rope  deteriorates  rapidly  when  exposed  to 
wind  and  weather,  and  for  this  reason,  when  practicable,  it  is 
tarred,  although  doing  so  weakens  it.  Hemp  should  only  be  used 
for  warps  and  bolt  ropes  of  sails,  as  it  is  much  :oo  hard  for  other 
purposes,  more  especially  when  wet. 

The  following  rules  give  the  equivalent  circumference  of  tarred 
and  white  hemp  rope  for  a  working  load  in  tons  of  one  third  the 
breaking:  si  ress  :  — 


\J~  x  load  =  circumference  of  white  rope. 
\/$  x  load  =  circumference  of  tarred  rope. 


392 


The   Naval   Constructor 


Other  Rope.  — A  variety  of  small  stuff  is  used  in  ship  work 
for  sundry  purposes,  the  principal  kinds  of  which,  and  their 
purposes,  follow  :  — 

Cotton  Rope  is  only  used  for  halliards  and  sheets  in  small  craft, 
being  much  softer  than  Manila. 

Housrline  is  used  for  lacing  sails,  etc. 

Marline  is  a  small  kind  of  tarred  hemp,  used  for  serving  ropes 
and  splices. 

Serving  twine  (tarred  or  waxed)  is  used  for  whipping  the  ends 
of  ropes  and  other  small  jobs. 


COIR    ROPE. 

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.   .   . 

LENGTH    OF   REEL 

For  100  Fathoms  of  Manila. 

(Cores  Q"  Diameter.) 


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18  0 

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17  9 

27  0 


Blocks  303 


CHAPTEE   II. 

BLOCKS. 

Blo<  C8  are  divided  broadly  into  two  varieties,  wood  and  iron, 
the  former  being  used  when  ree\  ing  fails  or  tackles  of  Manila,  and 
the  latter  for  wire  rope.  Wood  blocks  are  either  " made "  or 
"mortised,"  and  may  have  metal  or  lignum-vitae  sheaves.  The 
space  in  the  block  between  the  wood  and  the  sheave  is  called  the 
"  swallow,'"  the  opposite  end  of  the  block  being  named  the 
"  breech,'1  ami  the  sides  the  "  cheeks."  The  frame  of  the  block 
may  be  strapped  with  iron  or  rope,  a  score  being  cut  to  form  a 
housing  for  same. 

All  good  blocks  should  be  fitted  with  patent  roller  sheaves, 
especially  for  halliards  and  sheets,  or  for  any  heavy  work.  For 
topsail,  sheet,  throat  and  peak  halliard  purchases,  etc.,  ash  blocks, 
rope  stopped,  should  be  used.  For  derricks  on  freighters,  where 
wire  rope  is  used  for  heavy  loads,  iron  blocks  are  best;  where 
Manila  falls  and  topping  lifts  are  fitted,  wood  blocks  are  most 

suitable. 

It  will  be  evident  that  a  good  deal  of  power  can  be  wasted  by 

friction  of  the  sheave  on  pin,  and  also  by  the  rope  chafing,  through 
insufficient  ••swallow.'"  To  minimize  the  loss  due  to  friction 
through  the  former  cause,  the  pins  should  be  bushed.  Various 
bushings  are  employed  for  this  purpose,  probably  the  most 
efficient  being  a  gunmetal  or  bronze  sheave  with  spotted  graphite 
next  the  pin. 

The  loss  due  to  friction  is  10  per  cent  for  each  sheave. 

Blocks  are  designated  "single,"  "double,"  or  '-treble."  in 
accordance  with  the  number  of  sheaves  fitted,  and  are  variously 
named  to  denote  either  a  particular  shape  or  as  indicating  the 
purpose  for  which  they  are  intended.  Some  of  the  more  common 
ones  are  :  — 

Snatch  Blocks  are  used  to  divert  the  lead  on  the  hauling  part 
«»f  a  tall  or  tackle,  having  lor  this  purpose  a  hinged  part  on  one  of 
the  cheeks,  to  permit  ofplacing  the  rope  in,  which  would  other- 
wise require  reeving  —  a  tedious  and  often  impracticable  process. 
They  are  usually  fitted  at  heels  of  derricks,  and  on  deck,  to  take 
warping  and  other  Leads,  and  are  mostly  made  of  iron,  the  old- 
;  wood  snatch  block  l..  ing clumsy  and  eumbersome. 

Fiddle  Blocks  take  the  name  from  their  resemblance  to  the 
instrument,  being  constructed  with  two  sheaves  placed  tandem,  to 
permit  of  reeving  separate  halliards  leading  in  opposite  directions. 


394  The  Naval  Constructor 

They  are  to  be  found  on  peak-halliards,  at  preventer  stay  tackles, 
etc.,  and  are  made  in  wood  where  Manila  is  rove,  and  in  iron  for 
wire  rope. 

Gin  Blocks  are  used  on  derrick  heads  and  spans  in  conjunc- 
tion with  a  whip  for  handling  cargo,  and  comprise  a  skeleton  frame 
and  sheave  of  iron. 

Cat  and  Fish  Blocks  are  fitted  to  the  anchor  davit,  or  crane, 
and  consist  of  a  pair  of  blocks  with  double  or  treble  sheaves,  hav- 
ing a  large  swallow.  The  fish  (or  lower)  block  has  a  large  hook, 
sometimes  made  to  trip,  for  fishing  the  anchor  by  the  gravity  band 
on  the  stock.  These  blocks  are  made  in  both  wood  and  iron,  the 
latter  being  often  fitted  with  Manila  falls. 

Clump  Blocks  are  made  short  and  thick,  as  their  name  im- 
plies. They  are  used  for  tacks  and  sheets,  and  for  this  reason  are 
extra  large  in  the  swallow.     Made  in  wood  and  iron. 

Wrecking  Blocks  are  large,  extra  heavy  iron  strapped  blocks, 
with  lashing  shackles,  and  are  used  for  rigging  up  special  derricks 
for  temporary  use  with  heavy  loads. 

Cheek-Blocks  have  only  one  side,  the  other  cheek  being 
formed  by  fitting  against  a  spar. 

The  size  of  a  block  is  designated  by  the  length  of  the  shell,  and 
this  is  determined  from  the  circumference  of  the  rope  which  it 
reeves,  as  a  unit.  For  most  purposes  three  times  the  size  of  rope 
gives  a  suitable  block,  but  in  a  few  cases,  where  the  minimum  of 
friction  and  extra  ease  is  desired  in  the  swallow,  as  with  blocks 
for  boat  davit  tackles,  three  and  one  half  times  should  be  taken, 
e.g.,  a  block  for  ordinary  purposes  to  reeve  three-inch  Manila 
would  be  9  inches,  but  if  required  for  davit  falls,  the  size  would 
be  increased  to  10  inches.  The  diameter  of  sheave  is  usually 
about  two  thirds  of  the  size  of  block,  a  12-inch  block  having  an 
8-inch  diameter  sheave. 

In  ordering  blocks  it  is  necessary  to  prepare  a  list,  giving  a 
concise  but  full  and  exact  description  of  each  individual  block, 
embracing  the  following  points  :  — 

Sheaves. — The  number  of  sheaves  to  be  indicated  by  "S," 
"  D,"  or  "  T,1'  and  whether  of  lignum-vitse,  brass,  or  iron  sheaves, 
bushed  or  patent  roller  bushed. 

Name.  — The  purpose  for  which  the  block  is  intended  should  be 
given,  as,  "jib-sheets,"  "  derrick  falls,"  etc. 

Shackles  should  be  very  clearly  specified  where  they  are  for 
special  fittings.  Ordinarily  the  shackle  is  fitted  with  its  pin  at 
right  angles  to  the  axis  of  the  sheave,  this  being  the  most  natural 


Blocks  395 


way  to  engage  the  strap  of  block,  therefore  when  the  word 
"shackle,"  without  further  description,  is  used,  it  is  always  fitted 
in  this  manner.  Where,  however,  it  is  essential  to  have  it  with 
the  shackle  pin  running  parallel  with  Bheave  pin  (as  is  often 
necessary  to  get  the  falls  of  a  tackle  to  lead  in  line  with  hauling 
part)  the  words  "reverse  shackle  "  must  be  used.  If  the  shackle 
be  required  with  its  jaw  uppermost,  "reverse  upset  shackle" 
should  be  specified. 

It  often  happens  that  a  block  is  required  with  an  eye  to  engage 
a  shackle,  which  the  blockmaker  is  not  required  to  furnish.  In 
such  cases  it  is  well  to  state  whether  the  eye  should  be  "  worked  " 
or  a  "  shackle-eye  "  wanted.  A  "  worked  eye,"  of  course,  is  one 
having  its  edge  worked  round  like  a  ring,  the  "  shackle-eye"  being 
drilled  straight  through,  so  that  the  inserted  pin  bears  along  its 
entire  length.  For  a  given  diameter  of  pin,  that  in  a  shackle-eye 
would  be  twice  as  strong  as  the  one  bearing  on  a  worked  eye,  so 
that  where  other  considerations  do  not  count,  it  is  economy  to  fit 
a  shackle  eye. 

Beckets  are  small  eyes  fastened  at  the  breech  end  of  blocks 
to  take  the  thimble  on  the  standing  part  of  a  tackle.  They  are 
useful  to  have  on  all  spare  tackle  blocks. 

Strops.  —  "When  blocks  are  intended  for  brace  or  guy  pen- 
dants, they  should  be  specified  as  having  a  score  cut  to  receive  the 
rope  strop. 

Hooks  should  not  be  used  on  blocks  where  heavy  loads  are 
dealt  with.  For  loads  under  ten  tons  they  are  equally  reliable 
with  shackles,  besides  being  handier.  They  should  be  specified  as 
"loose,"  "  stiff  front,"  "side,"  or  "swivel "  hook,  as  required, 
and  the  working  load  given  in  all  cases,  as  many  of  the  hooks  on 
low  grade  blocks  are  considerably  inferior  in  strength  to  the  other 
parts  of  the  fitting. 

Sister,  or  Match  Hooks  are  used  for  a  variety  of  purposes, 
and  consist  of  two  honks  on  a  common  eye.  arranged  to  open,  and 
when  closed,  to  form  a  seemingly  solid  eye. 

Lashing  Shackles  are  especially  large  in  the  bow,  and  wider 
at  the  jaws,  than  ordinary  shackles,  being  fitted  to  the  heavier 
classes  of  double  and  treble  blocks,  to  permit  of  their  taking  a 
Manila  or  wire  rope  lashing. 

Swivel  Jaws  are  sometimes  fitted  to  the  upper  block  in  davit 
tackles. 

Appended  is  a  table  giving  actual  weights  of  blocks,  fitted  with 
shackles  and  beckets  complete,  which  will  be  of  use  in  estimating 
rigging  and  outfit  weights. 


396 


The  Naval   Constructor 


WEIGHT 


Kind  of 

Blocks. 

Single,  Double, 
ou  Treble. 

»2 

'A 
i— i 

H 
El 

rh 

— I 
H 

i 

if 

if 

3J 

c4 

N 

M 
II 

5 
5 
5 
5 
5 
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do 

pq 

M 

H 
K 

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S 

ii 

°.i 
ol 

-2 

3| 

5| 

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6 

6 

6 

6 

6 

6 

6 
6 
6 

DO 

M 

a 

X 

2 

2i 
4 

4£ 

4i 

6 

7 

12 

14 

K 

N 

as 

// 

7 

7 
7 
7 

7 

^7 
1 

7 
7 

7 

7 
7 
7 

M 

M 

H 

M 

O 

M 

si 

02 

// 

8 

8 
8 
8 
8 
8 
8 
8 
8 

8 

8 

8 
8 

W 
h! 

H 
K 
C 

H 

K 

s 

// 
9 

9 

9 

9 

9 

9 

9 

9 

9 

n 

H 
H 

w 

H 

K 
N 

M 

72 

to 

H 

M 

O 

H 

Wood   .... 
Wood   .... 
Wood   .... 

Wood   .... 
Wood    .... 
Wood    .... 

Wood   .... 
Wood    .... 
Cargo  block 
Gin 

Gin 

Iron  block    } 
Wire  rope    ) 
Iron  block    > 
Wire  rope     ) 
Iron  block   ) 
Wire  rope    ) 

Wood  snatch 
Iron  snatch . 
Rope  w.  iron 
Rope  w.  iron 
Rope  w.  iron 

S 
D 
T 
S 
D 
T 

D 

T 

S 
D 
T 

S 
D 
T 

II 

4 
4 
4 
4 
4 
4 

3 
5| 

6| 
6i 

91 
12| 

71 

10 
14 

9 
13 
19 

7£ 

10 

8i 

13 
18 

9* 
14£ 

20i 

12 

10 
18* 

28 

5i 
9 

ni 

10| 

16 

23J 

HI 

19 
27 

it 
10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

sheave 

10 
sheave 

10 
sheave 

10 

10 
10 
10 
10 
10 

6 

114 

15 

14 

25* 

35 

lGi 

29 

39 

19 
21 
40 
60 
100 

26i 
22 
38 
51 

Weight  of  Blocks 


397 


OF    BLOCKS. 


f. 


11 
11 
11 
11 
11 
11 


r. 

■— 

— 


20} 

31 
43 

23 
35 
47 


7. 


12 

12 
12 
12 
12 
12 
12 
12 
12 
12 
12 

12 

Bheave 

12 
Bheave 

12 
sheave 

12 
12 

12 

1-2 

12 

12 


II: 

20  i 
281 


33 

4.", 


r»o 
26 
23 


-". 


67 
100 

14.", 

■ 
81 


13 


30 

U 
62 

33 
47 

i  S 


14 
14 
14 
14 
14 
14 
14 
14 
14 
14 
14 

sheave 

14 

sheave 

14 

sheave 

14 

14 
14 

14 
14 

14 


y 


- 


20J 

35 
49 
39 

64 
89 
40 
73 
105 
: 
28 

150 

210 

4G 

56 

54 

100 

134 


y 

/.       - 


* 


15  44 

15  69 

15  100 

15  .".1 

15 

15 


15 


15 
15 
15 


GO 

06 

150 


•      y 

s 

53    - 


n; 

16 
16 

16  71 

It',  120 

16  166 

16  70 

16  52 


16  <r, 

16  86 

[6  90 

16  135 

16  210 


X       - 


18 

is 


188 


18     LOO 


18      90 

18     lor, 
18     150 


is 
18 


201 


y. 


s 
7 


20     130 


20 
20 


140 
147 


398 


The  Naval  Constructor 


STRENGTH  AND  WEIGHT  OF  RIGGING  CHAIN. 

(B  B  B  Quality.) 


*  Working  Load 

t  Breaking 

Weight 

Size. 

F.  S.  4 

Stress 

per  Foot  in 

in  Pounds. 

in  Pounds. 

Pounds. 

3 

1  6 

675 

2,700 

.5 

t 

1,260 

5,040 

.75 

5 

1,876 

7,504 

1.08 

2,660 

10,640 

1.50 

7 
1  6 

3,640 

14,560 

2.00 

1 

4,620 

18,480 

2.67 

9 

5,740 

22,960 

3.33 

5 

6,860 

27,440 

4.17 

11 

1  6 

8,120 

32,480 

5.17 

I 

9,800 

39,200 

6.18 

13 
1  6 

11,200 

44,800 

7.00 

7 

s 

12,460 

49,840 

8.00 

15 
1  6 

14,280 

57,120 

8.85    . 

1 

15,960 

63,840 

10.00 

1A 

17,640 

70,560 

12.00 

i| 

19,320 

77,280 

15.00 

H 

23,940 

95,760 

17.50 

n 

32,200 

128,800 

20.00 

if 

44,520 

178,080 

26.70 

2 

58,520 

234,080 

36.70 

*BB  quality  =  20%  less  than  table,    t  B  quality  =  30%  less  than  table. 


SIZE    OF    SHEAVES    FOR   IRON   BLOCKS. 


[AM. 

OF 
EAVE. 

IDTH 

OF 

OOVE. 

Size 

OF 

Chain. 

IAM. 

OF 

EAVE. 

IDTH 

OF 

OOVE. 

Size 

OF 

Chain. 

IAM. 

OF 

EAVE, 

IDTH 

OF 

OOVE. 

)IZE 

OF 

IAIN. 

A    a 

(U       Q 

n 

II 

a 

ii 

a 

a 

II 

II 

ii 

n 

3 

s 

... 

7 

H 

3 
5 

13 

2T96 

1  1 
16 

H 

\ 

... 

8 

H 

A 

14 

»* 

t 

4 

f 

.    .   • 

9 

if 

i 

5 

15 

3 

1  3 

16 

4f 

f 

3 

10 

2 

9 
16 

16 

3i 

7 
8 

5 

7 
% 

1 

11 

n 

5 

8 

17 

3i 

1  5 

16 

6 

1 

5 

T6 

12 

H 

1  1 

is 

18 

»i 

1 

Tackles 


399 


CHAPTER  III. 


TACKLES. 


100  LBS. 
PLUS  POWER 
APPLIED  TO   RAISE 


block,    therefore 

be  raised  by  the 

'•to,''    "from," 


50  LBS. 
TO  EALANCE 


SINGLEWHIP 


When  ropes  are  reeved  through  blocks  to  multiply  the  power  it 
is  proposed  to  apply,  the  combined  gear  constitutes  what  is  known 
as  a  tackle.  Th(  principle  of  the  block  and  tackle  is  the  distribu- 
tion of  weight  in  various  points  of  support, 
the  mechanical  advantage  derived  depend- 
ing entirely  upon  flexibility  and  tension  of 
the  rope,  and  the  number  of  sheaves  in  the 
moving  block,  hence  by  tackles  the  power 
is  to  the  weight  as  the  number  of  parts 
attached  to  the  moving 
(1)  divide  the  weight  to 
number  of  parts  leading 
or  "made  fast"  to  the 
moving  block,  and  the 
quotient  is  the  power  re- 
quired  to  produce  equi- 
librium —  omitting 
friction. 

(2)  Divide  the  weight 
to  be  raised  by  the  power 
proposed,  and  the  quo- 
tient is  the  number  of 
sheaves  in,  or  parts  at- 
tached to,  the  moving 
block. 

It  should  be  noted  that 
the  upper  block  of  a  tackle  has  to  bear  the 
weight  to  be  raised,  and  the  power  applied  to 
lift  it.  No  power  is  gained  by  increasing  the 
diameter  of  the  sheaves,  but  by  doing  so  you 
decrease  friction. 

In  arranging  the  blocks  for  a  purchase,  note 
that  the  hauling  part,  where  possible,  should 
lead  from  the  moving  block,  as  by  so  arrang- 
ing, the  power  is  increased. 

Tackles  are  named  variously,  sometimes  as  threefold,  fourfold, 
etc..  referring  to  the  number  of  ropes  rove  ;  and  as  guy-tackles, 
sheet-tackles,  etc.,  or  by  a  distinctive  name,  whose  derivation  in 
most  cases  is  obscure,  likp  Spanish  burton,  etc. 

A  single  whip  and  whip-upon-whip  are  shown  by  Figs.  272 
and  273  and  their  mechanical  advantage  indicated. 


Fig.  272. 


200  LBS. 


WHIP 
UPON 

V/HIP 


50  LBS. 


Fig.  273. 


400 


The  Naval  Constructor 


SINGLE 


SINGLE 


50  LBS. 


GUN 
TACKLE 

PURCHASE 


SINGLE 


200  LBS. 


Strictly  the  single  whip  is  not  really  a  tackle,  as  no  mechanical 
advantage  is  gained.  If  we  reverse  the  arrangement,  and  instead 
of  fixing  the  block,  we  make  one  end  of  the  rope  fast  and  haul 

on  the  other  after  it  is  rove  through  the 
block,  which  is  now  movable,  we  have  a 
tackle  with  the  power  applied  doubled. 

The  next  simplest  form  to  the  foregoing  is 
the  gun-tackle  purchase,  shown  by  Fig. 
274,  which  consists  of  two  single  blocks,  one 
movable  and  the  other  fixed.  In  the  dia- 
gram, the  power  is  shown  as  being  applied 
to  the  fixed  pulley,  which  results  in  doubling 
the  power  only.  If,  however,  the  order  be 
reversed,  and  the  rope  becketed  to  the  lower 
block,  from  which  the  hauling  end  would 
now  lead,  we  should  increase  the  power 
gained  so  that  150  lbs.  could  be  sustained 
in  equilibrium  by  the  application  of  50  lbs. 
In  all  tackles  the  hauled-  _ 
on  block  has  not  only  to 
support  the  load  pendant 
on  it,  but  also  the  powerDOUELE 
required  to  lift  the  load. 
The  luff-tackle  pur- 
chase shown  in  Fig.  275, 
Fig.  274.  -1S  aiso  known  as  a  watch- 

tackle,  and  has  exactly  the  same  mechanical 
advantages,  although  consisting  of  a  double  and 
single  block,  as  the  gun-tackle  with  the  hauling 
part  taken  from  the  movable  block,  that  is  to 
say,  the  power  applied  equals  one  third  of  the 
weight  to  be  raised.  The  case,  however,  is 
different  if  the  hauling  rope  of  the  luff -tackle 
be  taken  from  the  movable  block,  when  the 
ratio  of  power  to  weight  is  increased  to  one 
quarter. 

A  twofold  purchase  consists  of  two  double 
blocks,  and  has  a  ratio  of  power  to  weight  of 
one  quarter,  when  hauled  on  from  the  fixed 
block,  and  of  one  fifth  when  from  the  moving- 
block. 

A  threefold  purchase  comprises  a  pair  of  treble  blocks  with 
a  mechanical  advantage  of  one  sixth  leading  from  the  fixed  block, 
and  one  seventh  when  hauled  on  from  the  moving  block. 

Fig.  276  shows  a  single  Spanish  burton,  which  is  composed 
of   two  single  blocks  with   the  tackle  reeved   as   shown.     This 


50  LBS. 


LUFF 
TACKLE 
PURCH 


ASE 


Tackles 


401 


200  LBS. 


purchase  has  the  same  power  as  the  luff  tackle,  but  less  friction. 
It  is  a  handy  and  powerful  purchase,  used  for  doing  odd  jobs. 

The  double  Spanish  burton  is  made  up  of  a  luff-tackle  and  a 
whip,  with  the  standing  parts  toggled  on  together  to  the  becket  of 
the  lower  single  block.  It  has  the  same  power, 
but  with  much  less  friction,  as  a  threefold  pur- 
chase hauled  on  from  the  moving  block. 

Relieving    tackles     are     usually   two    or 

three-fold  purchase-,    having    the   fixed   block 

shackled  on  end  of  spare  tiller,  and  the  hauling 

block  made  fast  on  the  quarter.     These  tackles 

are  used  for  steering,  in  case  of  break-down, 

and  need  only  to  be  figured    for  the  steamer 

going  at  slightly  over  half  speed. 

A  tackle  may  be  attached  to  the  hauling  part 

of  another  tackle,  and  so  multiply  the  powers 

of  which  they  are  comprised. 

In  arranging  purchases  the  minimum  number 

of  sheaves  for  the  power 
required  should  be  used, 
and.  all  superfluous  fair- 
leads  dispensed  with,  as 
each  additional  sheave 
fitted  for  that  purpose 
absorbs  power. 

As  an  example  of  the 
application  of  the  fore- 
going notes  on  purchases 
to  the  finding  of  a  suitable  tackle  for  a  given 
load,  let  us  take  the  case  of  relieving  tackles 
on  tiller.  The  twisting  moment  on  the  rud- 
der head  is  first  calculated  by  the  rule  given 
on  page  106,  which  we  shall  assume  to  be 
150,000  inch-lbs.  With  a  spare  tiller  50 
inches  long  from  centre  of  stock  to  shackle 
eurton  pin,  we  should  have  a  net  load  of  3.000  lbs. 
to  move,  and  it  is  proposed  to  use  a  four- 
fold purchase  (i.e.,  2  double  blocks)  for  the 
purpose,  which  will  increase  the  load  by  four 
tenths  (4  sheaves  by  one  tenth  of  the  load 
Fig.  277.  each  for  friction),  making  the  actual  load  to 

be  operated  3,000  +  1.200  =  4.200  lbs.     The  moving  block  being 

on  the  tiller  head,  it  is  not  practicable  to  haul   from  it.  therefore 

we  have  only  4  parts  at  this  block.     Dividing  the  total  load  by 

four  ropes,  we  get  1,050  lbs.  (.47  ton)  tension  on  each  fall.     With 


DOUBLE 


400  LBS. 


SINGLE 


6!NGLE 


50  LBS. 


SINGLE 
SPANISH 
BURTON 


Fig.  276. 


50  LBS. 


DOUBLE 
SPANISH 


402  The  Naval  Constructor 


a  factor  of  safety  of  4£,  using  the  best  Manila  rope,  we  get  the 
equivalent  circumference  from  the  formula 

^tension  x  10  =   V-47  x  10  =  2|", 
say  2|",  as  the  manufactured  sizes  grade  by  quarters. 

The  size  of  the  double  blocks  to  take  the  rope  would  be  7  inches, 
obtained  by  the  rule  on  p.  394,  and  it  would  require  four  men  to 
handle  the  hauling  part. 

It  is  desired  to  lift  a  weight  of  12  tons  with  a  ship's  derrick,  and 
the  maximum  load  on  the  winch  must  not  exceed  5  tons;  required 
the  purchase,  size  of  steel  wire  rope  falls  and  blocks  ?  Owing  to 
the  heavy  load  dealt  with  in  this  case,  the  factor  of  safety  need 
not  exceed  5.  The  hauling  part  of  falls  to  be  led  through  a  lead- 
ing block  at  heel  of  derrick. 

Load  to  be  raised 12      tons 

Friction  of  5  sheaves 6         "■ 

Derrick  gear 4     " 

Total  load  to  overcome 18.4 

As  the  load  on  the  winch  may  nut  exceed  5  tons,  the  purchase 

18  4 
should  be  -j-^-  =  four  parts  in  the  falls  —  a  twofold  purchase. 

A  factor  of  safety  of  5  having  previously  been  decided  upon,  we 
get  for  the  breaking  stress  4.6  X  5=  23  tons,  and  the  equivalent  cir- 
cumference of  special  flexible  steel  wire  rope,  per  table  =  3  inches 
circ,  which  will  require  two  double  blocks  with  sheaves  13| 
inches  in  diameter.  It  should  be  noted  that  the  maximum 
tension  comes  on  the  hauling  part  in  hoisting,  but  on  the  standing- 
part  in  lowering. 

The  stress  on  topping  lift,  allowing  for  friction  of  one  sheave, 
and  power  applied  is  equal  to  9.4  tons,  requiring  special  flexible 
steel  wire  rope  of  3}/'  circumference. 

A  fourfold  purchase  rove  with  Manila  4"  circ.  having  two  12" 
double  blocks,  with  wide  mortise  and  the  hauling  part  taken  from 
the  moving  block,  will  be  suitable  for  the  load  of  9.4  tons  minus 
the  power  applied,  i.e.,  S\  tons. 

The  following  tables  give  the  strength  of  tackles  and  the  break- 
ing stress  from  actual  test  of  hooks  and  shackles,  fitted  by  the 
makers  to  the  various  sizes  of  blocks. 

The  proper  workingload  for  new  Manila  ropes  is  §  of  the  breaking 
stress.  Of  course,  first  grade  Manila  will  develop  a  greater  strength 
than  what  is  shown  by  the  accompanying  tables  of  tackles,  which 
are  based  on  the  strength  of  new  rope  adopted  by  the  manufac- 
turers, and  consequently  should  be  worked  to  when  figuring  the 
safe  working  load. 


Strength  of  Tackles  403 

Rule  to  find  the  equivalent  circumference  of  Manila  rope  for  a 
given  working  load  or  tension  (in  tons)  on  one  part  of  a  fall,  based 
on  a  factor  of  safety  of  3  :  — 

(  ircumference=  *s/lO  x  tension  which  is  very  easily  memorized. 

Inversely,  the  safe  working  load  for  a  given  circumference  of 
Manila  will  be 

— — -  =  safe  load. 
10 


404 


The   Naval   Constructor 


STRENGTH  OF  TACKLES. 
Ordinary  Blocks. 


o 

o 

pq 

0 
H 

02 
it 

3 

■  i— i 

1 

Two  Single 
Blocks. 

Two  Double 
Blocks. 

Two  Treble 
Blocks. 

Breaking- 
Stress  of 
Hooks  in 
Lbs. 

Breaking 

Stress  of 

Rope  in 

Lbs. 

Breaking 

Stress  of 

Hooks   in 

Lbs. 

Breaking 

Stress  of 

Rope  in 

Lbs. 

Breaking 

Stress  of 

Hooks  in 

Lbs. 

Breaking 
Stress  of 
Rope  in 
Lbs. 

1,143 

1,400 

1,492 

2,800 

2,219 

4,200 

81 

H 

1,492 

1,800 

2,218 

3,600 

2,985 

5,400 

4 

n 

2,218 

3,600 

2,985 

7,200 

3,987 

10,800 

5 

2 

2,985 

6,400 

3,987 

12,800 

5,410 

18,200 

6 

21 

3,987 

8,100 

5,410 

16,200 

6,360 

24,300 

7 

2f 

5,410 

12,100 

6,360 

24,200 

9,356 

36,300 

8 

o 
•J 

6,360 

14,400 

9,356 

28,800 

13,720 

43,200 

9 

3 

9,356 

14,400 

13,720 

28,800 

16,030 

43,200 

10 

31 

13,720 

19,600 

16,030 

39,200 

18,722 

58,800 

12 

4 

16,030 

22,500 

18,722 

45,000 

20,375 

67,500 

14 

41 

18,722 

28,900 

20,375 

57,800 

28,300 

86,700 

16 

5 

20,375 

40,000 
Twofold 

80,300 

80,000 

Fourfold 

35,680 

120,000 

Sixfold 

Strength  of  Tackles 


405 


STRENGTH    OF    TACKLES. 
Wide  Mortise    and  Heavy  Tackle. 


Size 

of 

Blo<  k. 

i            • 

—         H 

*  -  5 
s  -^ 

s  _ 

O      C 

TWO   Sin<;le 

Blocks. 

Two  Double 
Bloi  els. 

Two  TBEBIiE 

Blocks. 

Break- 
ing 

Stress  of 
Hoc  ks 
in  Lbs. 

Break- 
ing 

Stress  of 

Kope 

in  Lbs. 

Break- 
ing 

St  r.  «-  -.1 

Hooks 
in  Lbs. 

Break- 
ing 
Str<  SS 
of  Elope 

in  J 

Break- 
ing 

Str<  se 
of 

Hooks 
in  Lbs. 

Break- 
ing 
Stress  of 
Kope 
hi  Lbs. 

ir 

II 

i 

3 

6,300 

14,400 

9.350 

28,800 

13,720 

43,200 

8 

Si 

9,366 

19,600 

13,720 

39,200 

16,030 

58,800 

9 

81 

13,720 

19,600 

16,030 

39,200 

18,722 

58,800 

10 

4 

16,030 

22.500 

19,050 

45.000 

19,<)5<> 

07,500 

12 

4} 

19,050 

32.400 

20,375 

04,800 

28, 3' in 

97,200 

14 

5i 

28,300 

43.300 

35,080 

86,600 

35,080 

129.900 

10 

01 

35,680 

48,400 

Twofold. 

72,100 

96,800 

Fourfold. 

72,100 

145,200 

Sixfold. 

Wrecking  Blocks  and  Lashing  Shackles. 


ft                        M 

Two  Single 
Blocks. 

Two  Double 

Blocks. 

Two  Treble 
Blocks. 

Size 
Block. 

s§5 

s  - 
5    o 

Break- 
ing 
Stress  of 
Shackles 

in  Lbs. 

Break- 
ing 
Stress  of 
Rope 
in  Lbs. 

Break- 
ing 
Stress  of 
Shackles 

in  Lbs. 

Break- 
ing 
Stress  of 

Rope 
in  Lbs. 

Break- 
ing 

Sir ess  of 
Shackles 
in  Lbs. 

Break- 
ing 

Stress  ot 

K<  >pe 

in  Lbs. 

18 

7 

116,300 

67,600 

132,532 

135,200 

155,542 

202,800 

20 

8 

132,532 

78.400 

155,642 

156,800 

172,400 

235,200 

22 

n 

155,542 

115,600 

172.400 

231.200 

235,620 

340.  Miii 

24 

n 

172.400 

192.000 

Twofold. 

235,620 

384.000 

Fourfold. 

266,995 

570.000 

Sixfold. 

406 


The   Naval   Constructor 


DERRICK 

CAPACITY 


Item. 

2£  Tons. 

5  Tons. 

Topping  Lift  Purchase  .     .    j 

Fall  Blocks 

Topping  Lift  Blocks  .     .     . 
Purchase  Blocks    .... 

130'  of  2f"  G.S.W.R., 
single  whip,  170  lbs. 

65'  of  3"  G.S.W.R., 
single  whip,  110  lbs. 

60'  of  2\"  G.I.W.R., 
60  lbs. 

8'    0"   of    T9S"  crane 
chain,  25  lbs. 

30  fathoms  of  4"  Ma- 
nila, 90  lbs. 

60  fathoms  of  3"  Ma- 
nila, 96  lbs. 

2  @  50  lbs.  =  100  lbs. 

1@  60  lbs.  =  60  lbs. 

6  @  40  lbs.  =  240  lbs. 
100  lbs. 

130'  of  3"  G.S.W.R., 
single  whip,  220  lbs. 

65'  of  3£"  G.S.W.R., 
single  whip,  135  lbs. 

60'   of  2\"  G.I.W.R., 
60  lbs. 

8'    0"  of    if"  crane 
chain,  55  lbs. 

40  fathoms  of  4"  Ma- 
nila, 120  lbs. 

60  fathoms  of  3"  Ma- 
nila, 96  lbs. 

2  @  60  lbs.  =  120  lbs. 

1  @  70  lbs.  =  70  lbs. 

6  @  40  lbs.  =  240  lbs. 
150  lbs. 

Total  weight  of  gear  for  one 
boom,  excluding  wire  rope- 
reels,  forgings   to  mast  or 
boom,  gooseneck,  etc. 

1,051  lbs. 

1,266  lbs. 

Derrick    Rigging 


4U7 


RIGGING. 
OF  DERRICK. 


10  Toxs. 

20  T<  'vs.                                 50  T<  >NS. 

200'  of  3"  <t  S.W.R., 

gun  tackle.  4J5  lbs. 

1  _<»  «  t  3J"Q.S.WJR., 
gun  tackle,  '_u~»< )  lbs. 

6C  of  2}"  G.I.W.R., 
80  lbs. 

300'<.f  4"  G.S.W.R., 

lull"  tackle,  765  lbs. 

300^  3£"  G.S.W.R., 

tackle  rove,  630  lbs. 

eO'   of  3"    G.I.WJEL, 

UNI  U.S. 

710  oi :;'«;. r.s.w.K.  plough 
steel),  Mech.  adv.  <>l  tackle 
7=  1,200  lbs. 

540'  of  3"  G.P.S.W.R.,Mech. 
adv.  6  =  910  lbs. 

KMV   a   3£"  G.I.W.R.,  210  lbs. 

Shackles  used. 

40  fathoms  of  4"  Ma- 
nila, 1_'U  lbs. 

GO  fathoms  of  3"  .Ma- 
nila, 96  lbs. 

3  a  60  lbs.  =  ISO  lbs. 

2  7j  60  lbs.  =  120  lbs. 

6  a  40  lbs.  =  240  lbs. 
200  lbs. 

40  fathoms  of  4'   Ma- 
nila, 120  lbs. 

60  fathoms  of  ^"Ma- 
nila, 130  lbs. 

J®1!™**- 1=220  lbs. 

2  5    60  lbs.  ) 

2  2  100  lbs.  =  200  lbs. 

6  <g  40  lbs.  =  240  lbs. 
300  lbs. 

Direct  to  winch. 

100  fathoms  of  3£"  Manila, 
220  lbs. 

1  a  150  lbs. ) 

1  a   100  lbs.     =370  lbs. 
.  a  60    lbs.) 

i  a   50  lbs. ) 

2  5   100  Lbs.    =310  lbs. 
1   a  60    lbs.) 

4  a  40  lbs.  =  160  lbs. 

800  lbs. 

1,721  lbs. 

2.705  lbs. 

4. lso  lbs. 

Sectiox  V. 


CHAPTEE   I. 

EQUIPMENT. 

In  a  modern  steamship  the  Equipment,  as  understood  by  the 
classification  societies,  comprises  that  part  of  a  vessel's  outfit 
which  relates  to  the  handling  of  the  ship  and  the  safety  of  her 
complement,  and  in  Lloyd's  Register  is  represented  by  the  nu- 
meral "  1 "  after  the  character.  Under  this  heading  are  included, 
anchors,  chains,  hawsers,  boats,  steering  gear,  windlass,  and  the 
requirements  of  the  Board  of  Trade  Regulations  or  the  United 
States  Inspection  Laws. 

Lloyd's  Equipment. 

The  equipment  as  regards  anchors,  chains,  hawsers,  warps,  etc. 
is  regulated  by  the  number  produced  by  the  sum  of  the  measure- 
ments in  feet  arising  from  the  addition  of  the  half-moulded  breadth 
of  the  vessel  at  the  middle  of  the  length,  the  depth  from  the  upper 
part  of  the  keel  to  the  top  of  the  upper  deck  beams  (with  the 
normal  camber),  and  the  girth  of  the  half  midship  frame  section 
of  the  vessel,  measured  from  the  centre  line  at  the  top  of  the  keel 
to  the  upper  deck  stringer  plate,  multiplied  by  the  length  of  the 
vessel  for  a  one,  two,  and  three  decked  vessel  and  for  a  spar 
decked  vessel.  For  a  vessel  having  a  complete  awning  deck,  or 
a  continuous  shade  deck,  the  equipment  number  is  to  be  increased 
one-eighth  beyond  that  given  by  the  measurements  defined  above 
to  the  main  deck. 

For  a  steam  vessel  with  a  partial  awning  deck,  poop,  top  gal- 
lant forecastle,  bridge  house  or  a  raised  quarter  deck  the  equip- 
ment number  is  to  be  increased  beyond  that  for  a  flush  or 
spar-decked  vessel  by  that  proportion  of  the  addition  made  for  a 
complete  awning  deck  (i.e  ,  one-eighth)  which  the  combined  length 
of  the  erection  bears  to  the  length  of  the  vessel.  Where  erections 
are  fitted  upon  erections,  the  equipment  number  is  to  be  corre- 
spondingly  increased  in  the  same  proportion.  (Sect.  39  of  Lloyd's 
Rules.) 

409 


410 


The   Naval   Constructor 


LLOYD'S    EQUIPMENT 

Anchors  and  Stud  Cables, 

(Steamers 


NUM 

Bower  Anchors. 

stream  a.xi) 
Kedge  Am  h. 

Stud- 

NUMBEBS 

fob  ibon  and 
Steel 

BER. 

Ex.  Stock. 

Stockless. 

Ex.  Stock. 

1 

Vessels. 

M 

a 

- 

i   £ 

. 

>  2 
§5 

S 

bo 

2  2 

0 

OB 

O 

to 

.  1  s 
■s    3 

to     9 « 

s 

1  » 

j        3 
Cwt 

« 
Tons 

Cwt 

Cwt 

00 

0 

H 

Tons 

Cwt 

Cwt 

H 
Tons 

0 

Cwt. 

so 

0 

Tons 

a 
Fin 

s 

In" 

2,  <00  under  O,7o0 

2 

1 

L      3* 

K1S 

7 

4* 

617 

°50 

8| 

3 
4 

1 

120 

11 
16 

3,750  " 

4,630 

2 

1 

I      4J 

fil2 

"2  0 

85 

51 

7A1- 
1  5o 

10* 

11 

•  • 

1 
2 

. 

120 

12 
16 

4,030  " 

5,420 

2 

1 

L      5 

7-7- 
20 

10 

61 

fiio 
°5o 

12* 

1* 

Q18 

°2  0 

3 

4 

. 

135 

13 

16 

5,420  " 

6,150 

2 

1 

L      5| 

8 

11* 

71 

Q  9_ 
^2  0 

141 

1* 

■?18 
°5  0 

3 

4 

. 

165 

14 

T5" 

6,150  " 

6,840 

2 

1 

L       6* 

81 5- 

°20 

13" 

81 

10  7 

161 

2" 

4.10 

^20 

1 

. 

165 

IS 
16 

6,840  " 

7,490 

2 

1 

L       71 

Q  9 
a20 

14* 

9 

11  2 
Hon" 

18 

21 

415 

20 

1 

. 

165 

1 

7,490  " 

8,670 

3 

l  : 

I       8i 

10  t 
1U5B 

23* 

101 

12  * 

50 

291 

2* 

5 

u 

. 

165  Ii'b 

8,670  " 

9,770 

3 

l 

I    io 

12 

28* 

12* 

14260 

35*. 

3! 

623o 

i! 

4.  4 

*5o 

195  li2B 

9,770  " 

10,790 

3 

l 

I     12 

im 

34i 

15" 

16IQ 
0  n 

42f 

4 

6270 

2 

410 

^2  0 

195 

1t% 

10,790  " 

11,740 

3 

l 

L     13* 

ISA 

38* 

16f 

18'° 

48 

4! 

7  2 
<55 

25 

5 

210 

ll46 

11,740  " 

12,620 

3 

l   : 

I     I5i 

I     16f 

1GU 

43* 

19 

19*8 

541 

51 

711 
<20 

2i 

5 

210 

1A 

12,620  " 

13,450 

3 

l   : 

18 

47| 

20| 

21<?o 

59*. 

5* 

7*6 

<  20 

2! 

r.  5 
,J5o 

210  1T6S 

13,450  " 

15,120 

3 

l   : 

I     18 

19 

51i 

99i 

2 

Ol>15 

Z-20 

64 

6* 

OI6 

°5o 

9j 

°5o 

210  l/5 

15,120  " 

16,720 

3 

l   : 

I     21 

9112 

60 

261 

252§ 

75 

71 

Q_9_ 

3* 

K18 
d5o 

210 

1    8 
MB 

16,720  " 

18,260 

3 

l   : 

9}1 

L       -92 

9Q10 

— 32fl 

67 

291 

285V 

83| 

S 

10«2- 

lu20 

4 

6-^ 

240 

1    9 
ilS 

18,260  " 

19,780 

3 

i    ; 

L     251 

-'-'2  0 

72| 

31| 

29ig 

90! 

8* 

1012 

41 

fiI2 

u2li 

240 

110 

^is 

19,780  " 

21,280 

3 

l   ] 

[     27| 

26*§ 

79 

34* 

32  2 

98! 

8! 

11117 
lu2  0 

4* 

617 
2  0 

240 

111 

21,280  " 

21,220 

3 

l   ] 

30 

-^ 

85* 

37* 

34JO 

106! 

9* 

1111 

4! 

7  A 

20 

240 

112 
lT5 

24,220  " 

27,140 

3 

l   ] 

I     32 

r,.f)  2 

911 

40" 

35fg 

114 

10* 

19  8 

2  0 

51 

711 
20 

240 

113 
TB 

27.140  " 

30,020 

3 

l   i 

.     34 

■?1  12 
01 2  0 

97 

42* 

372  0 

1211 

10! 

1913 

51 

°2 

716 

50 

240 

1  I* 

30,020  " 

32,820 

3 

l   ] 

.     36* 

33  8 

104 

45* 

39fg 

130 

ill 

1352I 

5* 

71B 

270  1|| 

32,820  " 

35,450 

3 

l   1 

38" 

34lQ 
°0 

108J 

47*. 

405« 

1351 

11* 

13,7(1 

8 

270]  2 

35,450  " 

39,600 

l   i 

40 

35M- 

114 

50 

422  5 

142* 

12 

13i» 

6 

855o 

270  2r5 

39,600  " 

43,600 

3 

l   i 

43* 

38#5 

124 

54* 

45/0 

1  0 

1551 

12! 

1-^ 

6* 

oI5 
02.J 

270 

9-z- 

/16 

43,600  " 

47,400 

3 

l   1 

47 

40ll 

134 

58* 

«^-A  - 

472.0 

166| 

14 

15*0 

7 

955o 

270 

1)3 

-16 

47,400  " 

51,000 

3 

l   1 

51 

432° 

145* 

63*. 

50fg 

181 

151 

1614 

9  (I 

7* 

953 

270 

2l6 

51,000  " 

55,000 

o 

O 

l   1 

541 

45^j 

155* 

68 

52I0- 

193| 

16! 

18 

8 

1(>2V, 

270 

9  5 

-16 

55,000  " 

59,000 

3 

i    1 

58* 

47ig 

166* 

73 

5555o 

208 

18! 

I9*g 

9 

ll520 

300 

96 

■^16 

59,000  " 

63,000 

O 

l   i 

62 

49*8 

176* 

77* 

575(5 

220! 

20* 

91  _3_ 

-±2f 

10 

12 

300 

9  7 
-IB 

63,000  " 

67,000 

3 

l   1 

G6 

51*° 

188 

S2*. 

59*0 

235 

22 

99_7 

11 

12*? 

300 

9  8 
-16 

67,000  " 

71,000 

o 

l   1 

69* 

KQ10 

198 

87 

61*? 

248 

23*. 

9Q  1  0 

"°20 

12 

13*;. 

300 

9  9 

•^16 

71,000  " 

75,000 

3 

l   1 

73 

55^ 

208 

91 

63*§ 

259 

9fi  3 

13 

1 4  * s, 

330 

910 

75,000  " 

79,000 

3 

l   1 

76* 

57 

218 

95* 

n-i  1 

0950 

272 

27 

26  £ 

2  0 

14 

15*2 

330 

911 

—  1  A 

79,000  " 

83,000 

3 

l   i 

80 

58*8 

228 

100 

6725o-l 

285 

29 

27*0 

15 

16*8 

330  21| 

83,000  " 

87,000 

o 
O 

i   J 

B3* 

60  5  5 

238 

104* 

68*§ 

298 

30* 

29 

16 

17& 

330  2i| 

87,000  " 

91,000 

3 

l   1 

87"  i 

6115 

248 

109 

70*§ 

311 

■*9l 

9-2 

on10 

17 

ISA 

330  2l| 

91,000  " 

95,000 

3 

l   1 

90*! 

63^ 

258 

113 

79-2- 
<-20l 

322 

34 

0 1 0  0 

18 

19 

330  2i| 
330  316 

95,000  " 

99,000 

3 

l   i 

94  | 

65 

263 

1171 

r-ol6 

'92  0 

335 

36 

00  2 

19 

1QI7 

li'2il 

99,000  " 

103,000 

3 

l   l 

07* 

6626o 

278 

122 

'^50 

348 

37* 

01  2 

^"*2  0 

20 

onis 
-"20 

330  '3  A 

103,000  " 

107,000 

3 

l   l 

100* 

67595! 

286* 

125* 

76& 

357* 

39 

35^ 

21 

9112 

—  l*>i) 

330  3i26 

107,000  " 

111,000 

3 

l   l 

104 

68-ig 

296* 

130 

77*5 

370* 

41 

36^p, 

22 

99  _7 

--50 

330  3T35 

111,000  " 

115,000 

3 

li 

107* 

7051o 

306* 

134* 

79*% 

383| 

42* 

37*8 

23 

-35o 

330  3T45 

115,000  " 

119,000 

3 

ii 

111 

71/« 

316* 

139 

80*3 

396 

44* 

38*f, 

24  , 

9Q17 

-<J5o 

330  3rss 

119,000  " 

123,000 

3 

li  l 

114* 

72*§ 

326* 

143 

81*8 

407* 

46" 

39*: 

25  ! 

7415 

i-t20 

330  3T65 

123,000  " 

127,000 

3 

1 1 1 

118* 

74,% 

338" 

148 

83*°-! 

422" 

48 

41^ 

26  1 

25*§ 

330  3T7S 

127,000  " 

131,000 

3 

l   l 

122 

75^v 

348    152* 

84*2  434* 

49*  42,*. 

27  ' 

26^,  330  3ft 

Lloyd's   Equipment  Table 


411 


TABLE. 

Stream  Chain  and  Hawsers. 


Only.) 


101  f, 

'   < 

172  i  241T<„ 
176A  246fi 


(i7 
0  7  113 
0  7  113 
0  71  128 
0  7*  128 


90 

90 
90 
90  10 
90  10 
90  10 
90  11 
90  11 
90  12 
100  12 
100  12 
120  12 
120  13 
120  13 
120  14 
120  14 
120  15 
130  15 
130  15 
130  16 
130  16 
L30  16 
130  17 
130    .  . 
130    .  . 
130  .  . 
140   .  . 
140  .  . 
140   .  . 
140  .  . 
140  .  . 
140   .  . 
150  .  . 
150  .  . 
150  .  . 
150  .  . 


6 
6 
6 

7 
7 

7 
7 
7!. 
■\ 

■ 

n 

8 

8 

8 
8 


47  2  of  8 

59  2of8 

65  2  of  8 

71  2  of  8 

78  2  of  8 

2of8 

2  of  8 

85  2  of  8 

113  2of8 

113  2  of  8 

113 2  of  8 

U3  2of8 

r_',s:;.>rs 

128 3  of  8 
128 3  of  8 
l28  3of8 
128  3  of  8 
l28  3of8 
149 3  of  8 
149 3  of  8 
149 3  of  8 
149l3ofS 


4 

5 

5 

5 

5 

5 
2  of  5 
2  of  5 
2of5 
2  of  6 
2  Of  6 
2  of  6 
2of7 
2  of  7 
2of7 
2  of  7 
2of7 
2  of  7 
2oJ  8 
2of  8 
2  of  8 
201  8 
2 of  8  100 
■Jot's  Km, 

2  of  8  120 
2  of  8  120 
2 of 8  120 
2of8  120 

2  of  8  120 
_'ot  8  120 

3  of  8  120 
3  of  8  120 
3  of  8  120 
3of  8  l-o 
3of  8  120 
3of8  120 
3  of  8  120 


412  The  Naval  Constructor 


As  an  example  of  the  method  of  applying  the  foregoing  rule,  let 
us  take  the  case  of  a  3-deck  vessel,  having  a  complete  shelter- 
deck,  and  a  bridge  superstructure  with  houses  erected  on  it. 
This  type  will  clearly  exemplify  all  of  the  requirements  of  the 
rule,  as  we  shall  calculate  the  numeral  firstly  for  a  3-deck  vessel, 
to  which  we  will  then  add  one  eighth  for  the  complete  shelter- 
deck,  afterwards  increasing  it  by  the  proportion  that  the  length 
of  bridge  superstructure  bears  to  the  length  of  ship  (or  how 
much  of  another  eighth  we  shall  take),  and  finally  resolving  the 
area  of  the  deck  erections  or  superstructure  into  an  equivalent 
length  of  vessel  enclosing  the  same  area,  and  adding  its  propor- 
tionate value. 

Example :  —  Required  the  equipment  numeral  for  a  three- 
decked  vessel  having  a  complete  shelter-deck  on  which  is  built  a 
superstructure  having  deck  houses  on  top  :  — 

Dimensions  :  550'  x  65'  X  41'     to  shelter  deck 

33.5' to  upper   deck 
Length  of  superstructure      .     .  250' 
Size  of  deck  houses    .     .     .     .   100'  X  40' 

=  4,000  sq.  ft.  =i|oo  —  61,5'  equivalent  length 

Half-breadth 32.50' 

Depth  (to  U.DK+lGi"  camber),  34.85' 
Half  girth 63.00' 

130.35' 
Length x  550' 

71,692.5 

Add  |  for  complete  shelter 

deck 8,061.5 

Add  proportion  of  -|  repre- 
sented by  250'  of  super- 
structure         4,073.1 

Add  proportion  of  ^  repre- 
sented by  61.5'  equiva- 
lent length  of  houses  .     1,001.8 

Equipment  number    .     .     .  85,728.9 

The  preceding  "Table  22  "  of  Lloyd's  Rules  shows  the  require- 
ments of  that  Society  for  steam  vessels  based  on  the  above  rule. 


Equipment  Weights 


413 


EQUIPMENT    WEIGHTS. 

1'i.k   Lloyd' 8   1904   R\  i.i  s. 
Weights  in  Cwts.  of  112  Lbs. 


Equip- 

MK.NT 

Nu- 

\ \>    HORfc 

Sto<  k-. 

a  < 

Sti  d 
Link 
Cai 

5 

— 

TOWLINES. 

r 

**          * 

-  ( 

-  -    - 

j.  '—  r. 

-  =  z 
'-  ii 

ll  !   U  A!.. 

— . 

rf.~ 

—        P" 
— 

^  — 

2,750 

10.375 

1 1 

29,125 

3.9   ' 

1.35 

2.56 

3,750 

12.625 

■ . 

34.56 

8.0 

4.5 

2.46 

3.11 

4,630 

15.25 

it 

]  6 

45.77 

80 

1.  5 

m 

2.46 

3.80 

5.42') 

17.00 

64.35 

9.75 

5.35 

2.46 

4.05 

6,160 

20.00 

1  5 

1  •> 

74.48 

9.75 

6.15 

fe 

3.86 

5.70 

6,840 

22  06 

1 

84.15 

10.92 

7.4 

w 

4.66 

6.45 

7,490 

33.93 

lyV 

95.33 

14.56 

7.4 

A 

4.66 

7.80 

670 

42.38 

12*;.  25 

17.27 

8.4 

— • 

5.45 

10.00 

••'.770 

50.25 

1T-T 

141.14 

20.35 

9.5 

~ 

5.45 

11.45 

10,790 

57.06 

L68.00 

20.35 

9.5 

~. 

7.01 

12.65 

11,740 

63.93 

1 

185.61 

23.40 

12.6 

9.31 

14.75 

12,620 

60.84 

1  K 

203.16 

23.40 

12.6 

9.31 

15.95 

13,450 

76.18 

1    I 

■ 

222.40 

27.08 

13.9 

0.31 

17.45 

15,120 

88.46 

1    * 

242.04 

33  85 

8.4   1 

9.31 

10.10 

16,720 

98.75 

1-- 
1  8 

298.67 

38.25 

8  4 

9.31 

22.70 

18,260 

106.68 

1 

319.40 

38.25 

8.4 

18.62 

24.55 

10.780 

115.31 

in 

344.69 

43.33 

0.6 

g 

18.62 

2';.  60 

21,280 

124.59 

370.19 

..■>  .... 

18.62 

28.30 

24,220 

133.68 

1  i  s 

397  80 

18.55 

11.8 

-^ 

25.7 

30.00 

27,140 

141.58 

144 

1 

425.25 

48.55 

13.1 

— 

25.7 

32.70 

30.020 

L50.94 

1    ■ 

1 

511.375 

58.27 

1 3. 1 

— 

25.7 

37.96 

32,820 

156.82 

2 

538. 75 

65.14 

15  75 

29.6 

10.30 

35,450 

165.00 

■>  i 

- 

573.625 

65.14 

21.1 

29.6 

42.7n 

39,61  0 

179.31 

2  2 

- 

608.625 

65.14 

21.1    J 

29.6 

45.20 

414 


The   Naval   Constructor 


EQUIPMENT   WEIGHTS. 

Per  Lloyd's  1904  Rules. 
Weights  in  Civts.  of  112  Lbs. 


Equip- 
ment 

Nu- 
meral. 

Anchors 

and 
Stocks. 

Size 

OF 

Cable. 

Stud 

Link 

Cable. 

Stream 
Cable. 

co  o 
H 

Hawsers 

and 
Warps. 

3  =  * 

43,600 

193.00 

9  3 

645.75 

72.00 

22.8 

35.2 

48.50 

47,400 

209.44 

*A 

682.35 

72.00 

26.7 

35.2 

51.30 

51,000 

224.68 

2fV 

720.78 

79  54 

28.9 

35.2 

54.50 

55,000 

242.40 

9  6 

844.25 

106.06 

33.7 

45.2 

63.55 

59,000 

258  87 

2  "' 
16 

890.28 

106.06 

36.1 

45.2 

66.80 

63,000 

276.25 

2  8- 

^  1  6 

936.03 

116.09 

39.6 

45.2 

70.70 

67,000 

292.40 

9  9 
"IS 

983.00 

116.09 

39.6 

45.2 

73.80 

71,000 

307.15 

91  o 
z  re 

1,135.00 

126.75 

39.6 

45.2 

82.70 

75,000 

323.25 

211 

1,190.00 

138.25 

54.9 

45.2 

87.50 

79,000 

340.00 

012 
■^16 

1,247.00 

138.25 

54.9 

54.4 

91.70 

83,000 

356.10 

91  3 

1,304.00 

149.25 

54.9 

54.4 

95.90 

87,000 

372.85 

m 

1,362.00 

159.75 

54.9 

54.4 

100.10 

91,000 

387.00 

m 

1,422.00 

215.50 

66.0 

68.0 

107.90 

95,000 

403.75 

3 

1,482.00 

231.50 

66.0 

68.0 

112.50 

99,000 

420.00 

3TV 

1,543.00 

248.50 

66.0 

68.0 

117.20 

103,000 

432.50 

SA 

1,607.00 

248.50 

66.0 

81.6 

121.80 

107,000 

449.25 

3T36 

1,673.00 

265.75 

66.0 

81.6 

126.70 

111,000 

465.35 

^  -1 

1,739.00 

205.75 

66.0 

81  6 

130.80 

115,000 

481.60 

3  5 

1,805.00 

284.00 

69.5 

81.6 

136.00 

119,000 

496.25 

8A 

1,874.00 

284.00 

69.5 

81.6 

140.30 

123,000 

514.50 

3rV 

1,947.00 

299.25 

69.5 

81.6 

145.50 

127,000 

1 

to 

i- 530. 15 

»A 

2,020.00 

299.25 

69  5 

81.6 

150.00 

131,000 

American   Ship   Windlasses 


415 


AMERICAN    SHIP    WINDLASSES. 


Sll    \M 

s ii  km  Pump 

Lloi  D*8 

Si; 

CAP8TAH 

BRAKE 

'    I  1  •  M  1    \  ! 

<>i 

I'll  \1X 

I-:n..:m  ». 

WlMil.  \~-l   - 

Windlasses 

XUM  Bl  ic-. 

C  \r.i .i". 

Weight  in 

Weight 

Lbs. 

in  Lbs. 

t» 

// 

//             // 

Lbs. 

Lbs. 

6,150-  7.400 

l  5 

and  1 

1 

7,000 

:,.000 

7,490-  9,770 

1  h 

"    U 

4>     6 

8,500 

8,800 

9,770-11,740 

1 

••   M 

5x7 

9,000 

7,300 

11. 740-1:;.  450 

1A 

"   if 

G  x    8 

12,000 

9,000 

13,460-16,720 

] 

"   H 

7x8 

13,000 

12,260 

16.720-10.780 

i  9 

u      ]; 

8x    8 

17.000 

16,250 

19,780-24,220 

1  '  ] 

1 

11   ] , 

9x    8 

17.850 

17.100 

24.220-30.020 

111 

1  •'. 

1  s 

9x    9 

19,500 

18,750 

30,020-35,450 

1   '    " 

1 

..    2 

10  x  10 

27,000 

24.000 

35,45043,600 

2 

"    '2[ 

10  x  in 

23.<M)0 

31,000 

43,600-51,000 

2  A 

••    2i 

12  X  12 

31,000 

33,000 

51.000-50.000 

2  3 

ii 

12X12 

33,000 

35,000 

THE    SHAW  AND    SPIEGLE    PATENT    AUTOMATIC 
STEAM    TOWING    MACHINE. 


~ 

*- 

. 

- 

— 

c     ^ 

c      — 

W      ,     — 1 

c  x  - 

M       • 

H 

'.   s 

-  7 

fc 

—  —  — 

.>   —   — 

sj  x  gj 

—  —  — 

v    _  * 

-* 

;i 

-  1 

-  - 

- 

-  -  _ 

ii  <  ~ 

-  -  < 

«  ft  - 

Z  —  OB 

—     ->     — » 

- - 

— 
II 

- 

-      /. 

q    be 

i*^       ~ 

2 

- 

a     n 

a 

" 

n 

•1 

]      MS. 

i  a    i  a 

(1 

1 

-       8 

6,600 

2 

1'. 

2} 

\\ 

1,000  5  0>  ■"»  0 

1 

i; 

10>  10 

9,800 

2 

2 

2'. 

2 

2.5MO  •".  2  ■  5  8 

2 

i '. 

12x1 2 

14.50H 

21 

2J 

•_". 

1.500 

6  0xo  i» 

3 

i| 

14     14 

19,500 

->:■ 

- 

3 

-:■ 

6,000 

.7. 

'8.1 

.... 

4 

_' 

16x14 

21,500      2] 

2* 

3 

2  J 

.... 

•"> 

o 

16  •  16    18,000 

■  > 

3 

15,< 

.... 

416 


The   Naval   Constructor 


ADMIRALTY    CABLES, 

For  the  Dimensions  of  the  Common,  Enlarged  and  End 
Links,    and  of   the    Shackles  of   Chain   Cables,   for 
which  the  Cable-Holders  of  the  Various  Cap- 
stans and  Windlasses  are  Made. 


A. 

"3  » 
33  o 

Tn. 

^. 

A. 

m 
o 

A 

B. 

M 

O 

r— I 

O 

0) 
N 

33 

B. 

8. 

A 
*2 

In. 

C. 

a 

-.  a? 

60  <D 

J  X 

A 

c. 

y. 

A 

43 

In. 

D. 

J). 

I). 

X 

A 

43 

In. 

I). 

^^ 

43     — 

— *       »H 

In. 

I). 

>> 
A 

O 

% 

In. 

I). 

43   « 

bC  CD 

*A 

43    ~ 

blip 

v  +3 

_:  '■ 

H 

— 

H 

'-^ 
0 
V 

33 
in. 

'4-1 

li 

d  2 

'ohv 

*A 
In. 

Size  of 
Oval 
Bolt. 

In. 

In. 

in. 

111. 

In. 

In. 

In. 

f 
ii 

3.75 

2.25 

.69 

4.00 

2.50 

.750 

4.00 

2.50 

.812 

4.43 

2.5 

.875 

1.75 

1.0X   .75 

4.125 

2.475 

.76 

4.47 

2.75 

.825 

4.47 

2.75 

.894 

4.88 

2.75 

.96 

1.93 

1.1  X  .83 

? 

13 

4.50 

2.70 

.83 

4.88 

3.00 

.900 

4.88 

3.00 

.975 

5.33 

3.00 

1.03 

2.10 

1.2x   .9 

4.87 

2.98 

.90 

5.25 

3.25 

.98 

5.25 

3.25 

1.06 

5.77 

3.25 

1.11 

2.28 

1.3X   .98 

15 

5.25 

3.15 

.96 

5.69 

3.50 

1.05 

5.69 

3.50 

1.14 

6.21 

3.50 

1.23 

2.45 

1.4x1.05 

5.62 

3.38 

1.03 

6.09 

3.75 

1.18 

6.09 

3.75 

1.22 

6.m 

3.75 

1.37 

2.63 

1.5x1.13 

T5 

1 

6.00 

3.60 

1.10 

6.50 

4.00 

1.20 

6.50 

4.00 

1.30 

7.10 

4.00 

1.40 

2.80 

1.6x1.20 

6.38 

3.83 

1.17 

6.90 

4.25 

1.28 

6.90 

4.25 

1.38 

7.55 

4.25 

1.49 

2.98 

1.7x1.28 

116 

u 

6.75 

4.05 

1.24 

7.30 

4.50 

1.35 

7.30 

4.50 

1.46 

7.99 

4.50 

1.58 

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Admiralty    Rule   for    Links 


41 


A  A 


B  B 


GD)3 


^      £ 


CD 


Al 


L 


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Common  Link.     Enlarged  Link.  End  Link. 

Figs.  278-282. 


U 


3ZP 


- L_ 


-tHS- 


-7i1- 


s 


Sliackles. 


Note.  — The  dimensions  on  the  sketches  above  are  those  for  one-inch 
chain,  and  Bignify  so  many  diagrams  of  the  iron  of  the  common  links  ;  thus 
forming  a  Bcale  for  all  siz< 


418 


The   Naval   Constructor 


MUSHROOM  MOORING  ANCHORS. 


Weight 

EN  Lbs. 

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B. 

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Weight 
in  Lbs. 

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71 

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Mushroom    Mooring   Anchor  419 


420  The   Naval   Constructor 


CHAPTEE   II. 

BOATS. 

The  American  and  the  British  requirements  for  boats  carried 
by  foreign-going  steamships  are  practically  identical,  but  for 
vessels  employed  in  the  home  trade  there  is  much  dissimilarity. 
The  following  notes,  therefore,  where  they  refer  to  the  number  of 
boats  to  be  carried,  apply  only  to  ocean-going  steamships. 

Many  of  the  boats  carried  on  steamships  are  good  examples  of 
what  a  boat  should  not  be.  The  contractor  should  not  only 
supply  the  boat-builder  with  the  dimensions  of  the  boats  required, 
but  also  with  an  outline  of  the  mid  section,  more  particularly  in 
the  case  of  life-boats  and  dinghies.  In  many  cases  these  boats 
have  much  too  quick  a  rise  of  floor  line,  making  them  dangerous 
to  step  into  in  the  light  condition.  In  addition,  their  scantlings 
are  often  inadequate  for  working  boats  exposed  at  all  times  to 
the  extremes  of  weather.  With  a  view  to  supplying  a  good 
guide  as  to  what  are  wholesome  proportions  for  the  various 
classes  of  boats  hung  under  davits,  the  subjoined  diagram  has 
been  prepared  by  the  writer.  It  is  based  on  a  long  experience 
in  designing  and  building  these  craft. 

When  outline  plans  of  boats  are  prepared,  the  following  points 
should  be  noted :  — 


Minimum  clear  distance  between  thwarts,  2'  2".  Centre  of  row 
crutches  =  10"  abaft  aft  edge  of  thwarts.  Top  of  thwarts  or 
benches  =  9"  below  bottom  of  row  crutch.  In  single-banked 
boats  stroke  is  always  starboard.  Breadth  of  transom  =  §  rds. 
midship  top  breadth  (except  in  gigs).  Babbet  of  transom  = 
half  the  stern  depth  above  base.  Siding  of  hog  =  twice  the 
siding  of  keel.  Moulding  of  hog  =  .4  of  the  siding.  Scarphs  of 
keel,  etc.  =  4§  times  the  siding. 

Spars.—  Diameter  of  Mast,  \"     .     .     per  foot  of  length. 

"  Gaff,  Ty     ..."      "     "      " 
"         "  Topsaif  Yard,  \" 
"         "  Boom,  Ty  .     . 

"  Spread  Yard,  \" 
"         "  Bowsprit,  f"    . 

Sheer.  — Gigs   sheer  forward  .5"  per  foot  ;  aft  .25"  per  foot. 
Cutters     "         "         .43"    "       "    ;    "    .2"    »       " 
Dinghies  "         "         .53"    "      "    ;    "    .22"  '«      " 

Sheers  taken  with  L.W.L.  parallel  with  keel. 


It  C(  tt  tt 

it  tt  tt  tt 

tt  tl  tt  tt 

t  t  tt  t t  U 


Proportions  ot   Row   Boats 


421 


422 


The   Naval   Constructor 


Sails.  —  The  sail  area  may  with  advantage  be  based  on  the 
midship  section  area  measured  to  underside  of  thwarts  multiplied 
by  12.     i  x  12  =  sail  area. 

Scantlings.  —  The  scantlings  may  be  as  given  in  the  table 
which  shows  the  requirements  for  boats  of  the  Royal  Navy,  or 
these  may  be  modified  by  the  designer  in  accordance  with  his 
own  experience. 

Slings. —  Inspectors  should  insist  that  all  sling  plates  and 
lifting  rings  be  tested.  The  following  table  shows  the  tests  to 
which  these  fittings  are  usually  subjected  for  the  various  classes 
of  boats. 


TABLE    SHOWING   DIAMETER    OF   RING   BOLTS 

With  Proof  Test  to  be  Applied  and  the  Descrip- 
tions of  Boats  to  which  the  Various 
Sizes  are  to  be  fitted. 


Type  of  Boat. 

Length  of 
Boat. 

Diameter 

OF 

Bolt. 

Proof  Test. 

Dinghies 
Dinghies 
Cutter  gigs 
Galleys  .     . 
Gigs  .     .     . 
Whalers 
Cutters  . 
Cutters  .     . 
Cutters  . 
Cutters  . 
Cutters  . 
Cutters  . 

Feet. 

12 
14 

>      32  to  18 

J 

20,  18,  and  16 

23 

25  and  26 

27  and  28 

30  and  32 

34 

Inches. 

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2 

9 

1  6 

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1  1 
16 

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13 
1  6 

7 

8 

1 

18 

Tons. 
1 
1* 

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2 

9  1 

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21 

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5tV 

Position  of  Masts,  Tack  Blocks  and  Hooks  423 


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424 


The   Naval   Constructor 


DIMENSIONS    AND 


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Strakes,  No.,  about. 

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16 

15 

15 

15 

15 

15 

14 

14 

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No.  of  oars,  provision  ( 

14 

14 

12 

10 

10 

10 

10 

8 

4 

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to  be  made  for  .     .     | 

Dimensions  and   Scantlings   ot   Row    Boats    4l!o 


SCANTLINGS    OF   ROW    BOATS. 


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426 


The   Naval   Constructor 


YACHTS'   LAUNCHES. 


Length. 

Beam. 

Depth. 

Draft 
Aft. 

Weight 
Com- 
plete. 

Speed  in 
Knots. 

Class  of 
Machin- 
ery* 

16  0 

4  3 

1   10 

1     4 

Cwts. 

8| 

5 

H.P. 

5 

18  0 

4  6 

2     0 

1     6 

10 

6 

5 

20  0 

5  0 

2     2 

1     6 

12  . 

G 

5 

22  0 

5  3 

2     6 

1     8 

1G 

7 

10 

23  6 

5  4 

2     8 

2     0 

18 

n 

15 

25  0 

5  6 

2  10 

2     0 

10 

8 

15 

27  0 

6  0 

2  10 

2     4 

25 

10 

25 

30  0 

6  3 

3     0 

2     4 

30 

10 

25 

35  0 

6  6 

3     2 

2  10 

45 

12 

35 

45  0 

7  6 

4     0 

3     0 

90 

12 

50 

55  0 

8  6 

5     3 

3  10 

140 

12 

80 

*  Compound  engines  with  watertube  boilers. 


Standard   Ship's    Lite- Boat 


427 


428  The   Naval   Constructor 


CHAPTER   III. 

BRITISH   RULES   FOR    STEAMSHIPS    CARRYING 
PASSENGERS,    BOATS    AND   LIFE-SAVING 

APPLIANCES. 

'(a)  Ships  of  Division  A,  Class  1,  shall  carry  boats  placed  under 
davits,  fit  and  ready  for  use,  and  having  proper  appliances  for 
getting  them  into  the  water,  in  number  and  capacity  as  pre- 
scribed by  the  table  in  the  appendix  to  these  Rules  (see  page 
433)  ;  such  boats  shall  be  equipped  in  the  manner  required  by,  and 
shall  be  of  the  description  defined  in,  the  General  Rules  appended 
hereto. 

(6)  Masters  or  owners  of  ships  of  this  class  claiming  to  carry 
fewer  boats  under  davits  than  are  given  in  the  table  must  declare 
before  the  collector  or  other  officers  of  customs,  at  the  time  of 
clearance,  that  the  boats  actually  placed  under  davits  are  suf- 
ficient to  accommodate  all  persons  on  board,  allowing  10  (ten) 
cubic  feet  of  boat  capacity  for  each  adult  person,  or  "statute 
adult." 

(c)  Not  less  than  half  the  number  of  boats  placed  under  davits, 
having  at  least  half  the  cubic  capacity  required  by  the  tables, 
shall  be  boats  of  Section  A  or  Section  B.  The  remaining  boats 
may  also  be  of  such  description,  or  may,  in  the  option  of  the  ship- 
owner, conform  to  Section  C,  or  Section  D,  provided  that  not 
more  than  two  boats  shall  be  of  Section  D. 

(d)  If  the  boats  placed  under  davits  in  accordance  with  the 
table  do  not  furnish  sufficient  accommodation  for  all  persons  on 
board,  then  additional  wood,  metal,  collapsible  or  other  boats  of 
approved  description  (whether  placed  under  davits  or  otherwise), 
or  approved  life-rafts,  shall  be  carried.  One  of  these  boats  may 
be  a  steam  launch  ;  but  in  that  case  the  space  occupied  by  the 
engines  and  boilers  is  not  to  be  included  in  the  estimated  cubic 
capacity  of  the  boat. 

Subject  to  the  provisions  contained  in  paragraph  (/)  of  these 
rules,  such  additional  boats  or  rafts  shall  be  of  at  least  such 
carrying  capacity  that  they  and  the  boats  required  to  be  placed 
under  davits  by  the  table  provide  together  in  the  aggregate,  in 
vessels  of  5,000  tons  gross  and  upwards,  three  fourths,  and  in 
vessels  of  less  than  5,000  tons  gross,  one  half,  more  than  the 
minimum  cubic  contents  required  by  column  3  of  the  table.  For 
this  purpose  3  cubic  feet  of  air-case  in  the  life-raft  is  to  be  esti-? 
mated  as  10  cubic  feet  of  internal  capacity.  Provided  always  that 
the  rafts  will  accommodate  all  the  persons  for  which  they  are  to 


British    Rules  tor  Steamships  429 

be  certified  under  the  Rules,  and  also  have  3  cubic  feet  of  air-case 
for  each  person. 

All  such  additional  boats  or  rafts  shall  be  placed  as  conveniently 
for  being  available  as  the  ship's  arrangements  admit  of,  having 
regard  to  the  avoidance  of  undue  encumbrance  of  the  ship's  deck, 
and  to  the  safety  of  the  ship  for  her  voyagi  . 

(e)  In  addition  to  the  life-saving  appliances  before  mentioned, 
ships  of  this  elass  shall  cany  not  less  than  one  approved  life-buoy 
for  every  boat  placed  under  davits.  They  shall  also  carry  ap- 
proved life-belts,  or  other  similar  approved  articles  of  equal  buoy- 
ancy suitable  for  being  worn  on  the  person,  so  that  there  may  be 
at  least  one  for  each  person  on  hoard  the  ship. 

(/)  Provided,  nevertheless,  that  no  ship  of  this  class  shall  be  re- 
quired to  carry  more  boats  or  rafts  than  will  furnish  sufficient 
accommodation  for  all  persons  on  board. 

General  Rules. 

Boats.  —  All  boats  shall  be  constructed  and  properly  equipped 
as  provided  by  these  Rules,  and  all  boats  and  other  life-saving 
appliances  are  to  be  kept  ready  for  use  to  the  satisfaction  of  the 
Board  of  Trade.  Internal  buoyancy  apparatus  may  be  con- 
structed of  wood,  or  of  copper  or  yellow  metal,  of  not  less  than 
18  ounces  to  the  superficial  foot  or  of  other  durable  material. 

S<  don  A.  A  boat  of  this  section  shall  be  a  life-boat,  of  whale- 
boat  form,  properly  constructed  of  wood  or  metal,  having  for 
every  10  cubic  feet  of  her  capacity,  computed  as  in  Rule  2,  at 
least  one  cubic  foot  of  strong  and  serviceable  enclosed  air-tight 
compartments,  so  constructed  that  water  cannot  find  its  way  into 
them.  In  the  case  of  metal  boats,  an  addition  will  have  to  be 
made  to  the  cubic  capacity  of  the  air-tight  compartments,  so  as  to 
give  them  buoyanrv  equal  to  that  of  the  wooden  boat. 

Section  B.  A  boat  of  this  section  shall  be  a  life-boat,  of  whale- 
boat  form,  properly  constructed  of  wood  or  metal,  having  inside 
and  outside  buoyancy  apparatus  together  equal  in  efficiency  to 
the  buoyancy  apparatus  provided  for  a  boat  of  Section  A.  At 
least  one-half  of  the  buoyancy  apparatus  must  be  attached  to  the 
outside  of  the  boat. 

Section  C.  A  boat  of  this  section  shall  be  a  life-boat,  properly 
constructed  of  wood  or  metal,  having  some  buoyancy  apparatus 
attached  to  the  inside  and  (or)  outside  of  the  boat  equal  in  ef- 
ficiency to  one-half  of  the  buoyancy  apparatus  provided  for  a 
boat  of  Section  A  or  Section  B.  At  least  one-half  of  tin-  buoy- 
ancy apparatus  must  he  attached  to  the  outside  of  the  boat. 

S  ttion  1).  A  boat  of  this  section  shall  be  a  properly  con- 
structed boat  of  wood  or  metal. 


430  The   Naval   Constructor 


Section  E.  A  boat  of  this  section  shall  be  a  boat  of  approved 
construction,  form  and  material,  and  may  be  collapsible. 

Cubic  Capacity.  —  The  cubic  capacity  of  a  boat  shall  be 
deemed  to  be  her  cubic  capacity,  ascertained  (as  in  measuring 
ships  for  tonnage  capacity)  by  Simpson's  rule  ;  but  as  the  appli- 
cation of  that  rule  entails  much  labor,  the  following  simple  plan, 
which  is  approximately  accurate,  may  be  adopted  for  general 
purposes,  and  when  no  question  requiring  absolute  correct  ad- 
justment is  raised  :  — 

Measure  the  length  and  breadth  outside  and  the  depth  inside. 
Multiply  them  together  and  by  .6  ;  the  product  is  the  capacity  of 
the  boat  in  cubic  feet.  Thus,  a  boat  28  feet  long,  8  feet  6  inches 
broad,  and  3  feet  6  inches  deep,  will  be  regarded  as  having  a  ca- 
pacity of  28  x  8.5  X  3.5  =  491). 8,  or  500  cubic  feet.  If  the  oars 
are  pulled  in  rowlocks,  the  bottom  of  the  gunwale  of  the  row- 
lock is  to  be  considered  the  gunwale  of  the  boat  for  ascertaining 
her  depth. 

Number  of  Persons  for  Boats.  —  The  number  of  persons  a 
boat  of  Section  A  shall  be  deemed  fit  to  carry  shall  be  the  num- 
ber of  cubic  feet,  ascertained  as  above,  divided  by  10. 

The  number  of  persons  a  boat  of  Section  B,  Section  C,  Sec- 
tion D,  or  Section  E  shall  be  deemed  fit  to  carry,  shall  be  the 
number  of  cubic  feet,  ascertained  as  per  rule,  divided  by  8.  The 
space  in  the  boat  shall  be  sufficient  for  the  seating  of  the  persons 
carried  in  it,  and  for  proper  use  of  the  oars. 

Appliances  for  Lowering  Boats.  —  Appliances  for  getting  a 
boat  into  the  water  must  fulfil  the  following  conditions  :  —  Means 
are  to  be  provided  for  speedily,  but  not  necessarily  simultaneously 
or  automatically,  detaching  the  boats  from  the  lower  blocks  of  the 
davit  tackles  ;  the  boats  placed  under  davits  are  to  be  attached  to 
the  davit  tackles  and  kept  ready  for  service  ;  the  davits  are  to  be 
strong  enough  and  so  spaced  that  the  boats  can  be  swung  out  with 
facility  ;  the  points  of  attachment  of  the  boats  to  the  davits  are  to 
be  sufficiently  away  from  the  ends  of  the  boats  to  insure  their 
being  easily  swung  clear  of  the  davits  ;  the  boat's  chocks  are  to  be 
such  as  can  be  expeditiously  removed  ;  the  davits,  falls,  blocks, 
eyebolts,  rings,  and  the  whole  of  the  tackling  are  to  be  of  sufficient 
strength  ;  the  boat's  falls  are  to  be  long  enough  to  lower  the  boat 
into  the  water  with  safety  when  the  vessel  is  light.  The  life-lines 
shall  be  fitted  to  the  davits,  and  be  long  enough  to  reach  the  water 
when  the  vessel  is  light  ;  and  hooks  are  not  to  be  attached  to  the 
lower  tackle  blocks. 

Equipments  for  Collapsible  or  other  Boats,  and  for 
Life-Rafts.  —  In  order  to  be  properly  equipped,  each  boat  shall 
be  provided  as  follows  :  — 


Number  of  Persons  for   Life-Rafts       431 

[a  With  the  full  single-banked  complement  of  oars,  and  two 
spare  oars. 

(6)  Willi  two  plugs  f<»r  each  plug-hole,  attached  with  lanyards 

or  chains,  and  one  sel  and  a  half  of  thole  pins  or  crutches,  attached 
to  the  boat  by  sound  lanyards. 

(c)  With  a  sea-anchor,  a  baler,  a  rudder  and  a  tiller,  or  yoke 
lines,  a  painter  of  sufficient  length,  and  a  boat-hook.  The  rudder 
and  the  baler  to  be  attached  to  the  boat  by  sufficiently  long  lan- 
yards, and  kept  ready  for  use.  In  boats  where  there  may  be  a 
difficulty  in  fitting  a  rudder,  a  steering  oar  may  be  provided 
instead. 

d)  A  vessel  to  be  kept  filled  with  fresh  water  shall  be  provided 
for  each  boat. 

(e)  Life-rafts  shall  be  fully  provided  with  a  suitable  approved 
equipment. 

Additional  Equipments  for  Boats  of  Section  A  and 
Section  B. — In  order  to  be  properly  equipped,  each  boat  of 
Sections  A  and  B,  in  addition  to  being  provided  with  all  the 
requisites  laid  down  in  Rule,  shall  be  equipped  as  follows,  but 
not  more  than  four  boats  in  any  one  ship  require  to  have  this 
outfit,  and  where  boats  of  Sections  A  or  B  are  carried  in  lieu 
of  boats  of  Sections  C  or  D,  this  additional  outfit  need  not  be 
insisted  on  :  — 

(a)  With  two  hatchets  or  tomahawks,  one  to  be  kept  in  each 
end  of  the  boat,  and  to  be  attached  to  the  boat  by  a  lanyard. 

(6)  With  mast  or  masts,  and  with  at  least  one  good  sail,  and 
proper  gear  for  each. 

(c)  With  a  line  becketted  round  the  outside  of  the  boat  and 
securely  made  fast. 

(d)  With  an  efficient  compass. 

(e)  With  one  gallon  of  vegetable  or  animal  oil,  and  a  vessel  of 
an  approved  pattern,  for  distributing  it  in  the  water  in  rough 
weather. 

(/)  With  a  lantern  trimmed,  with  oil  in  its  receiver  sufficient 
to  burn  eight  hours. 

Number  of  Persons  for  Life-Rafts.  — The  number  of  persons 
that  any  approved  life-raft  for  use  at  sea  shall  be  deemed  to  be 
capable  of  carrying,  shall  be  determined  with  reference  to  each 
separate  pattern  approved  by  the  Hoard  of  Trade;  provided 
always,  that  for  every  person  bo  carried  there  shall  be  at  least 
three  cubic  feet  of  strong  and  serviceable  enclosed  air-tight  com- 
partments, constructed  so  that  water  cannot  find  its  way  into 
them.  Any  approved  life-raft  of  other  construction  may  be  used, 
provided  that  it  has   equivalent   buoyancy  to   that  hereinbefore 


432  The   Naval   Constructor 

described.  Every  such  approved  life-raft  shall  be  marked  in  such 
a  way  as  to  plainly  indicate  the  number  of  adult  persons  it  can 
carry. 

Buoyant  Apparatus.  —  Approved  buoyant  apparatus  shall  be 
deemed  sufficient,  so  far  as  buoyancy  is  concerned,  for  a  number 
of  persons,  to  be  ascertained  by  dividing  the  number  of  pounds  of 
iron  which  it  is  capable  of  supporting  in  fresh  water  by  32. 
Such  buoyant  apparatus  shall  not  require  to  be  inflated  before 
use,  shall  be  of  approved  construction,  and  marked  in  such  a 
way  as  plainly  to  indicate  the  number  of  persons  for  whom  it  is 
sufficient. 

Life-Belts.  —  An  approved  life-belt  shall  mean  a  belt  which 
does  not  require  to  be  inflated  before  use,  and  which  is  capable  at 
least  of  floating  in  the  water  for  24  hours  with  15  pounds  of  iron 
suspended  from  it.  Life-belts  are  to  be  cut  out  2  inches  under 
the  arm-pits,  and  fitted  so  as  to  remain  securely  in  their  place 
when  put  on. 

Life-Buoys.  —  An  approved  life-buoy  shall  mean  either:  (a) 
A  life-buoy  built  of  solid  cork,  capable  of  floating  in  water  for 
at  least  24  hours  with  32  pounds  of  iron  suspended  from  it ;  or 
(6)  A  strong  life-buoy  of  any  other  approved  pattern  or  material, 
provided  that  it  is  capable  of  floating  in  water  for  at  least  24 
hours  with  32  pounds  of  iron  suspended  from  it,  and  provided 
also  that  it  is  not  stuffed  with  rushes,  cork  shavings,  or  other 
shavings,  or  loose  granulated  cork  or  other  loose  material,  and 
does  not  require  inflation  before  use. 

All  life-buoys  shall  be  fitted  with  beckets  securely  seized,  and 
not  less  than  two  of  them  shall  be  fitted  with  life-lines  15  fathoms 
in  length. 


*&i 


Position  of  Life-Buoys  and  Life-Belts.  Water-tight 
Compartments.  — All  life-buoys  and  life-belts  shall  be  so  placed 
as  to  be  readily  accessible  to  all  persons  on  board,  and  so  that 
their  position  may  be  known  to  those  for  whom  they  are  intended. 

When  ships  of  any  class  are  divided  into  efficient  water-tight 
compartments  to  the  satisfaction  of  the  Board  of  Trade,  they 
shall  only  be  required  to  carry  additional  boats,  rafts  and  buoy- 
ant apparatus  of  one-half  the  capacity  required  by  these  Rules, 
but  the  exemption  shall  not  extend  to  life-jackets  or  similar 
approved  articles  of  equal  buoyancy  suitable  to  be  worn  on  the 
person. 

The  table  referred  to  in  the  foregoing  Rules,  showing  the  mini- 
mum number  of  boats  to  be  placed  under  davits  and  their  mini- 
mum cubic  contents,  follows  :  — 


Number  and   Capacity  of  Boats 


433 


BOAT    CAPACITY   FOR    STEAMERS. 
(British   Law.) 


GB T.'NNA'.K. 


Total 

BIlnimuk Kttk-  Minimum  Cubic 
bkb  of  <  "v tents 


10.000  ami 
9,0(Xi  and 
8,500  and 
8,000 
7. 7"  1 1 
7,500 
7,250 
7,000 
6.7.30 
6,300 
6,250 
6,000 
5 .  751 1 
5,500 

5.000 
4,750 
4,500 
4,250 
4,000 
3.750 
3,500 
3,250 
3.000 
2,750 

2,000 
1,750 
1,500 
1,250 
1,000 

iM  Ml 

SIMI 

700 

600 

4i«i 
300 
200 
100 


upwards 
upwards 


un 


ler  9.i Hid 
8,500 
8,000 
7 .  750 
7,500 
7,250 
7,0  10 
6,750 
.;.:,!  10 
6,250 
6,000 
5,750 
5,500 
5,250 
5,000 
4,750 
4,500 
4,250 
4,000 
3,750 
3,500 
3,250 
3,000 
2,750 
2,500 
2,250 
2,000 
1,750 
1,500 
1,250 
1,000 

800 
700 

600 

.-Mil 

41  HI 

300 
21 10 


Boats  to  be 

of  Boats  to  be 

I'i.a*  ED  rM'Ki; 

Placed 

Davits. 

im.kr  Davits 

L  X  B  X  D  X  .6 

2 

3 

16 

5,500 

14 

5,250 

14 

5,100 

14 

5,000 

12 

4.700 

12 

4.6U0 

12 

4,500 

12 

4.400 

12 

4,300 

12 

4. '200 

12 

4,100 

12 

4,000 

in 

3.700 

10 

3,600 

10 

3.500 

10 

3.400 

10 

3.300 

8 

2,900 

8 

2,900 

8 

2,800 

8 

2,700 

8 

2,600 

8 

2,500 

8 

'.'.400 

6 

2,100 

6 

2,050 

6 

2,000 

6 

1,900 

6 

1,800 

6 

1.700 

6 

1,500 

4 

1,200 

4 

1 J  iu0 

4 

900 

4 

800 

3 

700 

3 

6<HJ 

•_' 

400 

2 

350 

•_' 

300 

2 

251 1 

434  The   Naval   Constructor 


Note.  —  Where  in  ships  already  fitted  the  required  cubic  con- 
teuts  of  boats  placed  under  davits  is  provided,  although  by  a 
smaller  number  of  boats  than  the  minimum  required  by  this  table, 
such  ships  shall  be  regarded  as  complying  with  the  rules  as  to 
boats  to  be  carried  under  davits. 

In  case  of  vessels  under  200  tons  gross  tonnage,  the  capacity  of 
any  boat  to  be  supplied  should  not  be  less  than  125  feet.  If,  how- 
ever, in  any  case  this  rule  be  found  impracticable,  a  discretion  may 
then  be  exercised  by  the  Board  of  Trade. 

In  cases  where  a  small  vessel  is  unable  to  carry  more  than  one 
boat,  a  discretion  may  be  exercised  by  the  Board  of  Trade  ;  but 
whenever  one  boat  only  is  carried,  there  must  be  proper  provision 
to  enable  it  to  be  placed  readily  in  the  water  on  either  side  of  the 
ship. 

Capacity  and  Form  of  Life-Boats. — As  regards  the  boats  of 
Sections  A,  B,  C,  and  D,  Rule  1,  the  surveyors  will  see  that  the 
requirements  of  the  Rules  are  observed,  and  that  the  capacity  of 
the  boats,  and  the  number  of  persons  they  are  fit  to  carry,  are 
ascertained  by  Rules  2  and  3  (page  430).  In  measuring  boats 
the  length  and  breadth  are  to  be  regarded  as  the  "extreme  dimen- 
sions measured  to  the  outside  of  the  plank.  The  number  of  per- 
sons for  which  a  boat  is  to  be  passed  is,  however,  subject  to  the 
further  condition  that  the  space  in  the  boat  shall  be  sufficient  for 
the  seating  of  them  all,  and  the  proper  use  of  the  oars.  That  this 
requirement  is  fulfilled  must  be  ascertained  by  practical  experi- 
ment in  all  cases  before  a  declaration  is  granted,  unless  one  or 
more  boats  in  a  ship  are  of  the  same  pattern,  when  only  one  of 
such  boats  need  be  tested.  Life-boats  (except  those  of  Section  C) 
should  be  built  whale-boat  fashion,  both  ends  alike.  In  ships 
which  have  been  fitted  with  boats  previous  to  the  Rules  coming  into 
force,  square-sterned  boats  need  not  be  condemned  if  fitted  with 
the  required  amount  of  buoyancy,  but  all  life-boats  of  Sections  A 
and  B  subsequently  supplied,  or  supplied  to  new  ships,  must  be 
built  whale-boat  fashion.  All  collapsible  boats,  and  all  boats 
whether  collapsible  or  not,  if  constructed  of  any  material  other 
than  wood  or  metal,  must  be  in  accordance  with  a  pattern  approved 
by  the  Board  of  Trade  before  they  are  passed  as  a  portion  of  the 
life-saving  appliances  required  by  the  Rules. 

Stowage  of  Boats.  —  All  boats  required  by  the  Rules  to  be 
placed  under  davits  are  to  be  kept  fit  and  ready  for  use  ;  and  when 
they  are  swung  inboard  and  resting  on  the  chocks,  the  chocks  are 
to  be  so  constructed  that  the  boat  can  be  at  once  swung  outboard 
without  requiring  to  be  lifted  by  the  tackles  —  i.e.,  it  shall  not  be 
necessary  to  take  more  than  the  weight  of  the  boat. 

The  manner  in  which  the  additional  boats,  not  requiring  to  be 


Lifeboat   Buoyancy  430 

placed  under  davits,  are  to  be  stowed,  will  vary  in  different  ships, 
but  they  must  be  stowed  to  the  satisfaction  of  the  surveyors,  so  as 
to  be  as  readily  available  for  use  as  is  practicable,  having  due  con- 
sideration tn  the  circumstances  mentioned  in  the  Rules. 

In  all  cases  where  boats  are  stowed  on  skids,  a  batten  and  space 
platform  of  about  2£"  planks  should  be  fitted  from  skid  to  skid, 
under  and  alongside  the  boat,  when  being  launched  forward  or  aft, 
and  as  a  platform  for  the  men. 

Equipments.  —  The  equipments  for  all  boats  are  provided  for 
in  the  Rules,  and  surveyors  are  to  see  that  the  requirements  are 
carefully  complied  with.  The  painters  for  boats  are  not  to  be  less 
than  20  fathoms  in  length. 

When  the  Rules  require  a  life-boat  of  Section  C  to  be  carried, 
and  owners  choose  to  provide  a  boat  of  Section  A  or  J5,  the  addi- 
tional equipments  required  by  General  Rule  6  for  boats  of  Section 
A  and  Section  B  need  not  be  insisted  on. 

Rudder.  —  In  some  of  the  collapsible  boats  it  is  difficult  to  fit 
a  rudder  ;  in  this  case  a  steering  oar  properly  fitted  may  be  passed 
instead. 

Buoyancy.  —  The  buoyancy  of  life-boats  of  Section  B  must  be 
partly  inside  and  partly  outside  the  boat,  and  a  boat  in  which  it  is 
wholly  inside  or  wholly  outside  shall  not  be  passed  as  a  boat  of 
S      ion  B. 

In  the  case  of  life-boats  of  Section  C,  one-half  the  buoyancy 
must  be  outside  the  boat ;  the  remainder  may  be  either  inside  or 
outside,  or  partly  inside  and  partly  outside. 

The  inside  buoyancy  for  boats  of  Sections  A,  B,  and  C,  must 
consist  of  strong  and  serviceable  enclosed  air-tight  compartments, 
such  that  water  cannot  lind  its  way  into  them. 

The  outside  buoyancy  for  boats  of  Section  B  must  consist  of 
Bolid  cork  covered  with  canvas,  and  painted  and  attached  to  the 
outer  skin  of  the  boat  to  the  satisfaction  of  the  surveyors,  both  as 
regards  its  position  and  also  as  regards  its  attachment.  No  other 
material  is  to  be  used  unless  expressly  sanctioned  by  the  Board  of 
Trade.  The  outside  buoyancy  must  be  equal  to  at  least  half  the 
buoyancy  required  for  boats  of  Section  .1.  and  the  inside  and  out- 
side buoyancy  together  must  equal  in  efficiency  the  buoyancy  re- 
quired for  a  boat  of  Section  A. 

To  effect  this  1.25  cubic  feet  of  cork  is  to  be  considered  as 
equivalent  to  1  cubic  foot  of  air-case. 

The  foregoing  remarks  apply  to  outside  buoyancy  for  boats  of 
Section  C.  excepting  that  the  total  buoyancy  is  only  required  to 
be  half  that  of  boats  of  Section  A  or  Section  B.  When  the  solid 
cork  is  not  permanently  attached  to  the  side  of  the  boat  in  such  a 


436  The  Naval  Constructor 

manner  that  moisture  cannot  collect  between  the  two  surfaces,  it 
will  require  to  be  removed  every  time  a  declaration  is  granted  to 
ascertain  (1)  whether  the  cork  is  becoming  sodden  ;  (2)  whether 
moisture  is  collecting  between  the  cork  and  the  skin  of  the  boat, 
and  in  that  way  rotting  the  wood.  The  consideration  (2)  will  not 
apply  to  metal  boats. 

Air-Cases,  Material  and  Construction. —  Air-cases  are  re- 
quired by  the  Rules  to  be  constructed  of  wood,  or  of  copper  or 
yellow  metal  of  not  less  than  18  ounces  to  the  superficial  foot,  or 
of  other  durable  material. 

The  average  weight  of  18  ounce  copper  air-cases  is  about  5 
pounds  per  cubic  foot,  and  if  air-cases  of  other  material  exceed  this 
weight,  the  cubic  capacity  of  the  air-cases  must  be  correspondingly 
increased. 

As  yellow  metal  in  time  becomes  extremely  brittle,  copper  is  far 
preferable.  Zinc  is  not  durable  material,  and  should  not  be 
passed  ;  neither  should  galvanized  iron  or  steel  cases  be  passed 
for  new  boats. 

A  note  should  be  made  in  each  district  of  all  ships  whose  boats 
are  already  tilled  with  galvanized  iron  or  steel  air-cases,  with  a 
view  to  their  being  frequently  inspected.  Steel  or  iron  air-cases 
previously  passed  of  less  thickness  than  21  ounces  are  not  to  be 
rejected  so  long  as  they  continue  in  good  condition. 

Copper  and  yellow  metal  air-cases  are  to  be  made  with  proper 
hook  joints  not  less  than  three-eighths  of  an  inch  in  width,  ham- 
mered well  down  and  soldered,  and  no  other  joint  is  to  be  passed 
unless  specially  approved  by  the  Board  of  Trade. 

The  cases  are  not  to  exceed  four  feet  in  length  ;  they  are  to  be 
substantially  enclosed  with  wood,  which  is  to  be  close-jointed  so 
as  to  cover  any  exposed  part  of  the  air-case,  and  the  wood  form- 
ing the  top  is  not  to  be  less  than  one  inch  in  thickness. 

The  coverings  in  the  boats  over  the  air-cases  should  be  secured 
with  brass  screws,  so  as  to  enable  the  cases  to  be  removed  with- 
out difficulty  for  examination,  and  no  air-case  which  is  not  en- 
closed from  the  outer  shell  of  the  boat  should  be  passed. 

Spaces  filled  with  or  containing  any  material  are  not  to  be  deemed 
air-spaces  unless  specially  approved  by  the  Board  of  Trade. 

Copper  or  yellow  metal  air-cases  must  not  be  carried  in  con- 
tact with  the  skin  of  the  metal  boats. 

Where  boats  not  required  by  the  Rules  to  be  fitted  with  air- 
cases  are  so  fitted,  as,  for  instance,  in  some  of  the  collapsible  or 
semi-collapsible  boats,  these  provisions  as  to  air-cases  need  not  be 
insisted  upon. 

Steam  Launches,  etc.,  Carried  by  Steamships.  —  In  the 

cases  of  launches  or  other  boats  propelled  by  steam  power,  which 


Life- Rafts,   Buoyant  Apparatus  437 

are  carried  as  part  of  the  additional  boat  equipment  required  by 
the  Rules  made  under  the  provisions  of  the  Merchant  Shipping 
Act,  an  inspection  of  the  boat,  machinery,  and  boilers,  and  of  the 
mounting  and  fitting  thereof,  should  be  made.     Strain  launches 

must  not  be  passed  as  a  part  of  the  boat  equipment  required  to  be 
under  davits. 

In  case  of  any  vessel  provided  with  a  steam  launch  or  boat  in 
addition  t<>  the  boat  rapacity  required  under  the  Rules,  the  sur- 
veyors need  1 1 « » r  interfere  unless  they  have  reason  to  believe  that 
there  is  some  defect  in  the  boat,  machinery,  or  boiler,  or  in  the 
fittings  or  arrangement  thereof,  which  might  be  dangerous  to 
life. 

Boats  Already  Supplied.  —  Iu  carrying  these  instructions 
into  effect,  surveyors  are  to  be  careful  not  to  interfere  unnecessa- 
rily with  boats  supplied  before  November,  1800,  but  in  the  case  of 
new  boats  coming  under  survey  for  the  first  time,  as  well  as  in 
all  cases  in  which  the  fittings  of  the  boats  require  renewal,  the 
Rules  contained  in  these  instructions  are  to  be  strictly  adhered  to. 

Appliances  for  Lowering  Boats.  —  These  appliances  must 
be  in  accordance  with  Rule  4.  of  the  General  Rules,  and  must,  in 
the  surveyor's  opinion,  be  such  as  not  to  endanger  human  life. 
They  should  be  tested  at  each  survey  for  renewal  of  a  passenger 
certificate. 

The  question  of  determining  whether  the  requirements  of  the 
Rules  respecting  appliances  for  lowering  boats  are  complied  with 
in  the  case  of  any  particular  kind  of  gear  coming  under  the  sur- 
veyor's notice,  shall  be  left  to  the  principal  officers  of  the  districts. 

In  order  to  insure  uniformity  of  practice,  each  principal  officer, 
who  may  pass  any  particular  disengaging  gear,  should  request  the 
maker  to  supply  50  copies  of  the  plans  and  specifications  for 
distribution  among  the  surveyors  in  the  several  districts.  These 
copies  should  be  sent  to  the  Board  of  Trade  by  the  Principal 
officer,  together  with  his  report  upon  the  gear.  No  certificates 
of  approval  for  disengaging  gear  will  be  issued. 

The  Principal  ()fficer\should  also  report  to  the  Board  of  Trade 
when  any  particular  disengaging  gear  has  been  inspected  and 
deemed  unsatisfactory  or  unsafe,  and  should  explain  fully  in  such 
report  the  details  winch,  in  his  opinion,  render  it  undesirable. 
No  formal  certificate  of  approval  will,  however,  be  granted  by 
the  Board  of  Trade  or  their  officers  for  any  special  kind  of  gear. 

Life-Rafts,  Buoyant  Apparatus.  — No  part  of  the  gear  which 
is  intended  to  bear  the  weight  of  the  boat  must  be  made  of  cast 
iron,  and  life-rafts  are  to  be  approved  by  the  Board  of  Trade  ; 
they  are  to  be  supplied  with  a  suitable  equipment  to  the  satisfac- 


438  The   Naval   Constructor 


tion  of  the  surveyors,  and  this  must  include  a  sea-anchor,  not  less 
than  20  fathoms  of  hawser,  and  oars  in  proportion  to  the  size  of 
the  raft. 

The  number  of  persons  that  any  approved  life-raft  for  use  at 
sea  is  to  be  deemed  capable  of  carrying  is  the  number  that  the 
raft  is  able  to  seat  safely,  provided  always  that  for  every  person 
so  carried  there  are  at  least  three  cubic  feet  of  strong  and  service- 
able enclosed  air-tight  compartments. 

Approved  buoyant  apparatus  is  to  be  deemed  sufficient  for  a 
number  of  persons  to  be  ascertained  by  dividing  the  number  of 
pounds  of  iron  which  it  is  capable  of  supporting  in  fresh  water  by 
32,  provided  also  that  the  sides  and  ends  of  the  apparatus  shall 
afford  a  space  of  one  horizontal  foot  for  each  person  for  whom  it 
is  certified,  and  that  a  line  for  the  people  to  cling  to  is  properly 
becketted  all  round  it.  Such  buoyant  apparatus  shall  not  re- 
quire to  be  inflated  before  use,  and  shall  be  of  approved  con- 
struction. 

Marking.  —  Surveyors  will  note  that  rafts  and  buoyant  ap- 
paratus shall  be  marked  in  such  a  way  as  to  plainly  indicate  the 
number  of  adult  persons  for  which  they  are  deemed  sufficient. 
Plates  will  be  supplied  by  the  Board  of  Trade  to  be  screwed  on  to 
the  woodwork  of  both  rafts  and  buoyant  apparatus,  indicating 
this  number  ;  and  forms  of  demand  (surveys  116  for  rafts  and  116a 
for  buoyant  apparatus)  for  plates,  to  be  filled  up  and  returned  to 
the  Board  of  Trade,  will  be  issued  for  the  use  of  the  Principal 
Officer.  No  raft  or  buoyant  apparatus  is  to  be  regarded  as  finally 
approved  until  the  marking-plate  has  been  affixed. 

Air-Cases  of  Rafts,  etc.  —  The  instructions  in  the  case  of  life- 
boats apply  equally  to  life-rafts  and  buoyant  apparatus,  so  far  as 
the  length,  weight  and  enclosure  of  the  air-cases  are  concerned, 
excepting  that  as  life-rafts  and  buoyant  apparatus  are  only  in- 
tended to  be  used  in  cases  of  extreme  need,  and  are  consequently 
not  exposed  to  the  same  wear  and  tear  as  the  life-boats,  a  mini- 
mum weight  of  16  ounces,  copper  or  yellow  metal,  may  be  passed. 

Life-Belts.  —  No  life-belt  is  to  be  passed  that  is  not  capable  of 
floating  in  fresh  water  for  24  hours  with  15  pounds  of  iron  sus- 
pended from  it.  It  should  be  cut  out  2  inches  under  the  arm- 
pits, and  fitted  so  as  to  remain  securely  in  its  place  when  put  on. 
When  any  other  material  than  solid  cork  is  used  for  buoyancy,  it 
must  be  specially  approved  by  the  Board  of  Trade.  All  new  life- 
belts should  be  fitted  with  adjustable  shoulder-straps. 

It  is  desirable  that  notices  should  be  posted  indicating  the  place 
of  stowage  of  any  belts  which  are  not  plainly  visible  to  pas- 
sengers. 


Life- Buoys  439 

Life-Buoys.  —  No  life-buoy  stuffed  with  rushes  or  with  cork 
shavings  or  other  shavings,  or  granulated  cork,  or  any  loose 
material,  is  to  I"-  passed.  All  eork  life-buoys  are  to  be  built  of 
solid  cork,  and  fitted  with  lines  becketted  and  securely  seized  to 
the  life-buoy,  and  none  are  to  be  passed  that  will  not  float  for  24 
hours  in  fresh  water  with  32  pounds  of  iron  suspended  from  them. 
If  life-buoys  are  not  inade  of  solid  cork,  the  pattern  and  material 
must  be  approved  by  the  Board  of  Trade.  No  contrivance  is  to 
be  passed  as  a  life-buoy  that  requires  inflation  before  use.  Life- 
buoys are  to  be  secured  by  a  tousle  and  becket,  or  auy  other 
similar  method,  so  that  they  can  be  quickly  released  ;  they  must 
not  be  lashed  or  seized  to  the  rail  or  any  part  of  the  vessel,  but 
must  be  kept  so  as  to  be  ready  for  use  at  a  moment's  notice  in 
case  of  an  emergency. 

Not  less  than  two  of  the  life-buoys,  one  on  each  side  of  the 
ship,  are  to  be  fitted  with  life-lines  15  fathoms  in  length. 

Oil-distributing  Apparatus.  —  Vessels  for  distributing  oil 
are  to  be  to  the  satisfaction  of  the  surveyors,  and  are  to  be  so  con- 
structed as  to  distribute  the  oil  evenly  and  gradually  on  the  sur- 
face of  the  water. 


440 


The   Naval   Constructor 


CHAPTER   IV. 


UNITED    STATES    NAVIGATION    LAWS    RELAT- 
ING  TO    BOATS    AND   LIFE-SAVING 
APPLIANCES. 

The  British  requirements  as  to  the  build  of  boats,  number  of 
oars,  life-lines,  and  the  rule  for  calculating  the  capacities  of  life- 
boats, are  similar  to  the  American  regulations,  excepting  that  for 
river  steamers  the  capacity  is  divided  by  7  to  give  the  number  of 
persons  carried. 

Boat  Ladders.  —  Where  ladders  or  steps  are  necessary  to  en- 
able passengers  on  board  to  escape  conveniently  to  the  life-boats, 
such  steps  shall  be  provided  and  placed  on  each  side  of  the 
steamer,  with  manropes  of  suitable  size  and  of  sufficient  length 
to  reach  the  water ;  and  one  of  the  means  of  escape  from  one  deck 
to  another  shall  be  near  the  stern  of  the  vessel. 

Relieving  Tackle.  —  Extra  steering  apparatus  for  all  steamers 
carrying  passengers,  consisting  of  relieving  Jackles  or  tiller,  must 
be  provided. 

Metal  Life-Boats  must  be  constructed  of  good  iron  or  other 
suitable  metal  not  less  in  thickness  than  18  B.W.G. 

Davits.  —  All  life-boats  must,  if  possible,  be  carried  on  cranes 
or  davits  ;  but  if  impossible  so  to  carry  all  the  life-boats  required, 
the  remainder  must  be  stowed  near  at  hand,  so  as  to  be  easily  and 
readily  launched  when  required. 

River  Steamers.  —  Steamers  navigating  rivers  only  (except 
ferry-boats,  canal-boats,  and  towing-boats,  of  less  than  50  tons) 
must  have  one  good  substantial  boat.  The  cubic  capacity  of  such 
boat  as  found  by  the  rule  given  on  p.  444  divided  by  7  will  deter- 
mine the  number  of  persons  to  be  carried. 

Freight,  Canal,  and  Towing  Steamers.  —  Freight,  canal, 
and  towing  steamers  of  less  than  50  tons  must  be  equipped  with 
boats  or  rafts,  as,  in  the  opinion  of  the  inspectors,  may  be  neces- 
sary, in  case  of  disaster,  to  secure  the  safety  of  all  persons  on 
board. 

Excursions  by  Permit.  —  Steamers  making  an  excursion 
under  a  permit  must  have  at  least  one  life-boat,  and  shall  be 
equipped  with  other  life-boats,  or  their  equivalents,  as,   in  the 


Lite-Boats  for  Ocean   Steamers  441 


judgment  of  the  inspectors,  will  best  secure  the  safety  of  all  per- 
sons on  board  in  case  of  disaster. 

Automatic  Plug.  —  All  metal  life-boats  hereafter  built  shall 
be  furnished  with  an  automatic  plug. 

River  Passenger  Steamers.  —  Passenger  steamers  navigat- 
ing rivers  (excepting  steamers  of  100  gross  tons  and  under,  here- 
inafter provided  for)  must  be  supplied,  in  addition  to  the  boat 
required  in  the  paragraph  '•  River  Steamers,"  with  life-boats  in 
proportion  to  their  tonnage,  as  follows  : 

Steamers  over     100  and  not  over     300  gross  tons     .   1  boat. 
Steamers  over     300  and  not  over     000  gross  tons     .  2  boats. 
Steamers  over     (Jim  and  not  over     900  gross  tons     .  3  boats. 
Steamers  over      900  and  not  over  1,200  gross  tons     .  4  boats. 
Steamers  over  1,200  gross  tons 5  boats. 


Aggregate  Capacity.  —  The  aggregate  capacity  of  life-boats 
on  steamers  navigating  the  Ked  River  of  the  North  and  rivers 
whose  waters  flow  into  the  Gulf  of  Mexico  and  their  tributaries, 
shall  not  be  less  than  120  cubic  feet  to  each  boat  for  the  number 
of  boats  as  given  in  the  table  ;  and  for  life-boats  on  steamers  navi- 
gating other  rivers  than  those  named,  the  aggregate  capacity  shall 
not  be  less  than  180  cubic  feet  to  each  boat  as  given  in  the  table  ; 
and  where  smaller  life-boats  are  employed  for  either  class  of 
river  steamers,  their  aggregate  capacity  shall  not  be  less  than  the 
aggregate  capacity  of  the  larger  boats  ;  provided,  however,  that 
river  steamers  required,  under  the  table,  to  carry  more  than  two 
boats,  may,  where  the  owners  prefer  to  do  so,  supply  the  boat 
capacity  above  that  number  with  a  good,  substantial  life-raft  or 
rafts,  such  raft  or  rafts  to  be  of  an  aggregate  carrying  capacity  not 
less  than  that  of  the  boats  so  omitted. 

Capacity  may  Equal  Complement.  —  No  steamer  embraced 
in  the  foregoing  section  shall  be  required  to  have  more  life-boats, 
or  of  a  greater  capacity,  than  sufhVient  to  carry  the  passengers 
allowed  by  the  certificate  of  inspection  (including  the  crew).  One 
of  the  life-boats,  unless  exempted  by  the  supervising  inspector, 
must  be  made  of  metal. 

Life-Boats  for  Ocean  Steamers. —  The  total  capacity  of  life- 
boat-, or  of  life-boat-  and  life-rafts,  on  steamers  navigating  the 
ocean  (except  steamers  of  100  ."  >ss  tons  and  under,  hereinafter 

provided  for),  shall  not   be  less  than  the  capacity  given,  according 
to  tonnage,  in  the  following  table  : 


442 


The   Naval   Constructor 


BOAT    CAPACITY    FOR    OCEAN    STEAMERS. 

(American  Law.) 


Gross  Tonnage. 


Steamers  over  : 

100  and  not  over 

200 

300 

400 

500 

1,000 

1,500 

2,000 

2,500 

3,000 

3,500 

4,000 

5,000 

5,500 

6,000 

6,500 

7,000 

7,500 

8,000 

8,500 

9,000 

9,500 
10,000 
10,500 
11,000 
11,500 
12,000 
12,500 
13,000 
13,500 
14.000 
14,500 
15,000 


a 

1 t 
it 

ti 
11 
ii 
1  I 
I . 
ii 
u 
k 
c  t 
11 
tl 
It 
i ; 
u 
i . 
u 
u 
ti 
({ 

it 

.  1 
it 
1 . 
it 
tt 


it 
(( 

u 
1. 

II 

11 

1 1 

u 

1 1 

u 

t . 

i. 

(i 

t. 

ii 

ii 

u 

1 1 

ii 

• . 

.i 

1 1 

u 

u 

ii 

u 

1 1 

i  1 
11 
11 


200 

300 

400 

500 

1,000 

1,500 

2,000 

2,500 

3,000 

3,500 

4,000 

5,000 

5,500 

6,000 

6,500 

7,000 

7,500 

8,000 

8,500 

9,000 

9,500 

10,000 

10,500 

11.000 

11,500 

12,000 

12,500 

13,000 

13,500 

14.000 

14.500 

15.000 


Total  Capacity 

of  Boats 
in  Cubic  Feet. 


540 

720 
1,080 
1,260 
1,620 
1,800 
2,160 
2,340 
2,700 
2,880 
3,240 
3,420 
3,870 
4,320 
4,770 
5,220 
5,670 
6,120 
6,570 
7,020 
7,470 
7.920 
8,145 
8,370 
8,595 
8,820 
9,045 
9,270 
9,495 
9,720 
9,945 
10,170 
10,395 


Note.  — Not  more  than  one-third  of  the  boat  capacity  required  on  ocean 
steamers  may  be  substituted  by  its  equivalent  in  approved  life  rafts  or 
approved  collapsible  (folding)  life-boats. 

These  boats  must  be  of  suitable  dimensions,  and  each  not  less  than  180 
cubic  feet  capacity.    (For  good  proportions  of  boats,  see  diagram  on  p.  421.) 


Lite-boats  of  Lake,  Bav,  and  Sound  Steamers  443 


LIFE-BOATS    FOR    STEAMERS    NAVIGATING 
NORTHWESTERN    LAKES,    BAYS,    AND 

SOUNDS. 


N  i  > .  <  >  i  • 

C  UP  A<   ITV 

Gross  TONNAGE. 

Boats. 

of  Boats. 

Steamers  over : 

Cu.  Ft. 

100  and  not  over      200 

2 

360 

200     "         "            300. 

3 

640 

300     ••         "            4(H). 

4 

720 

400     ••         "            500. 

5 

900 

500     ••         "         1.000. 

6 

1,080 

1,000     "         ••         1,600. 

7 

1,260 

1.500     "         ••         2.000. 

8 

1.440 

2.000     ••         ••         2.500. 

9 

1,620 

2.500     ••         "         3,000. 

10 

1,800 

3,000     ••         "        3,600. 

11 

1,980 

3,500      •         "        4.000. 

12 

2,160 

4,000     ••         "        4,500. 

13 

2,340 

4.. 500     ••          ••         5.000. 

14 

2.835 

5.i  )(X)     "         ••         5.500. 

15 

3,330 

Note  on  Table.  —  Steamers  above  5,600  gross  tons  shall  be 
furnished  with  an  additional  boat  of  not  less  than  405  cubic  feet 
capacity  for  each  additional  500  tons  burden,  or  fraction  thereof  ; 
or  if  the  owners  or  agents  prefer,  two  boats  may  be  used;  pro- 
vided, the  aggregate  capacity  shall  be  the  same  as  the  one  boat 
described. 

These  boats  shall  be  substantially  built  with  reference  to  the 
trade  in  which  the  steamer  is  engaged,  and  shall  not  be  of  less 
dimensions  than  20  ft.  x  5  ft.  3  ft.,*  unless,  where  smaller  life- 
boats are  employed,  their  aggregate  capacity  shall  equal  the  aggre- 
gate capacity  of  the  larger  boats  ;  provided,  hoivever,  that  no 
steamer  shall  be  required  to  have  more  life-boats  than  sufficient  to 
carry  the  passengers  she  is  allowed  by  the  certificate  of  inspection, 
together  with  her  officers  and  crew. 

Not  more  than  one  third  of  the  boat  capacity  required  on  lake, 
bay.  and  sound  steamers  may  be  substituted  by  its  equivalent  in 
approved  life-rafts  or  approved  collapsible  (folding)  life-boats. 


*  For  good  proportions,  see  diagram  on  page  421. 


444  The   Naval  Constructor 


Marking  of  Boats.  — All  wood  boats  required  on  steam-ves- 
sels shall  have  branded  or  cut  on  the  stem  thereof  the  net  cubic 
feet  contents  of  such  boats,  figured  as  follows  : 

Multiply  the  outside  length,  outside  width,  and  inside  depth 
together  and  the  product  by  .6,  and  divide  the  product  by  10  for 
ocean,  lake,  bay,  or  sound  steamers  ;  and  for  river  steamers,  di- 
vide the  product  by  7  ;  the  quotient  will  be  the  number  of  persons 
such  a  boat  is  allowed  to  carry. 

Example.  — The  carrying  capacity  of  a  boat  20  feet  in  length, 
5  feet  b*  inches  in  breadth,  and  2  feet  3  inches  deep,  will  be  deter- 
mined as  under : 

For  ocean,  lake,  bay,  or  sound  steamers, 

20  x  5.5X2.25  X  .6      148.5      _ 
z— =  =15  persons. 

For  river  steamers,  same  boat,    — —  =  21  persons. 

Metal  boats  shall  have  net  cubic  feet  measurement  painted  on 
stem  in  black  letters  and  figures  not  less  than  f  inch  high  on  a 
white  ground. 

Every  life-raft  shall  have  stencilled  on  it  in  a  conspicuous  place 
(the  number  of  persons  it  can  carry,  as  determined  by)  the  net 
cubic  feet  contents  as  per  ratio  in  the  following  paragraph  : 

Life-Raft  Capacity. — All  life-rafts  and  floats  shall  have  an 
actual  buoyancy  of  187J  lbs.  upon  oceans  for  every  person  al- 
lowed, and  156  lbs.  upon  lakes,  bays,  sounds,  and  rivers  for 
every  person  allowed.  kSuch  life-rafts  and  floats  must  be  suitably 
equipped  with  life-lines  and  oars. 

All  rubber  and  canvas  rafts  shall  be  kept  inflated  at  all  times, 

Life-Floats.  —  When  wooden  life-floats  are  required  on  steam- 
vessels,  in  compliance  with  law  they  shall  be  at  least  of  the  follow- 
ing dimensions,  or  other  proper  dimensions  of  equal  cubical  capac- 
ity, viz.,  4  feet  in  length,  14  inches  in  breadth,  and  2  inches  in 
thickness.  These  floats  shall  be  made  of  white  pine  wood,  or  any 
other  wood  not  exceeding  white  pine*  in  weight  per  cubic  foot. 

Drags,  or  Floating  Anchors.  —  Drags,  or  floating  anchors, 
shall  be  constructed  so  as  to  be  capable  of  being  compactly  stowed 
near  the  head  of  the  ship.  (For  a  detail  of  these  anchors,  see  p. 
363.) 

Steamers  navigating  the  ocean  must  be  provided  with  at  least 
one  drag,  of  area  as  follows  :  —  For  steamers  of  400  gross  tons  and 

*  What  is  known  as  white  pine  in  the  States  is  called  yellow  pine  in  the 
British  Isles. 


Drags  or   Floating  Anchors  445 

under,  not  less  than  25  superficial  feel  ;  for  steamers  of  over  400 
gross  tons,  the  area  of  drag  shall  not  be  less  than  thai  deter- 
mined by  adding  to  25  square  feel  "lie  .square  foot  for  each  addi- 
tional 25  gri  iss  tons  above  400  tons. 

Example.  —  The  area  of  a  drag  on  a  vessel  of  1,000  tons  will 
equal :  — 

n.      1,000-400      ._  ,    . 

25  -1 ^ =41*  square  feet. 

Steamers  of  over  5,000  tons  gross  may  be  equipped  with  two  or 
more  drags,  provided  the  t < »tal  area  is  not  less  than  thai  required 
by  this  rule.  Steamers  whose  routes  do  uot  extend  off  anchor- 
age are  not  required  to  have  drags,  or  floating  anchors,  on  board. 

(A  table  giving  areas  for  sea-anchors  based  on  the  above  rule  is 
given  «'ti  p.  362.) 

Every  life-preserver  adjustable  to  the  body  of  a  person  .-hall 
be  made  of  good,  sound  cork  blocks  or  other  suitable  material, 
with  belts  ami  shoulder  straps  properly  attached,  and  shall  be  con- 
structed so  as  to  place  the  cork  underneath  the  shoulders  and 
around  the  body  of  the  person  wearing  it,  the  shoulder  straps  to 
be  sewed  <  in  at  least  eight  inches  apart  on  the  back  <  if  the  preserver, 
and  sewed  together  at  an  angle  where  they  cross  the  body,  and 
must  also  have  a  strap  across  the  breast  from  one  shoulder  strap 
to  the  other,  sewed  fast  at  one  end  and  with  a  buttonhole  at  the 
other,  with  a  button  on  shoulder  strap  to  which  the  cross  piece 
can  be  buttoned,  and  all  belt  life-preservers  shall  be  not  less 
than  54  inches  in  length,  measurement  from  end  to  end  around 
the  body.  Ami  it  shall  be  the  duty  of  the  inspectors  to  see  by 
actual  examination  that  every  such  life-preserver  contains  at  least 
six  pounds  of  good  cork,  which  shall  have  a  buoyancy  of  at  least 
four  pounds  to  each  pound  of  cork.  Inspectors  are  further  re- 
quired to  see  such  life-preservers  are  distributed  throughout  the 

cabins,    stater is,    berths,    and    other    places    convenient    for 

passengers  on  such  steamer;  and  there  shall  be  a  printed  no1 
posted  m  every  cabin  and  stateroom,  and  in  conspicuous  places 
about  the  decks,   informing  passengers  of  the  location  of  life- 
preservers  and  other  life-saving  appliances,  and  of  the  mode  of 
applying  or  adjusting  the  same.     Cork  cushions,  when  constructed 
of  good,  sound  cork  blocks  or  other  suitable  material,  with  belts 
and  shoulder  straps  properly  attached,  said  cushions  to  contain 
not  less  than  six  pounds  of  cork,  when  passed  by  local  inspectors, 
may  be  used  in  lieu  of  life-preservers  on  small  pleasure  steam. 
Barges  towed  by  steamers  and  carrying  passengers  on  i   a 
"night  routes"  .-hall  have  a  life-preserver   tor  each   passenger; 
and,  in  addition  thereto,  .shall  be  supplied  with  a  yawl  boat,  ten 
buckets  and  three  ax<    . 


446 


The   Naval   Constructor 


Every  sea-going  steamer  and  every  steamer  navigating  the  great 
Northern  and  Northwestern  lakes  carrying  passengers  shall  have 
not  less  than  three  water-tight  cross  bulkheads.  Such  bulkheads 
shall  reach  to  the  main  deck  in  single -decked  vessels,  otherwise  to 
the  deck  next  below  the  main  deck.  For  wooden  hulls  they  shall 
be  fastened  to  suitable  framework,  which  framework  must  be 
securely  attached  to  the  hull  and  caulked.  For  iron  hulls  they 
shall  be  well  secured  to  the  framework  of  the  hulls  and  strengthened 
by  stanchions  of  angle  iron  placed  not  more  than  two  feet  from 
centre  to  centre.  One  of  the  bulkheads  must  be  placed  forward 
and  one  abaft  of  the  engines  and  boilers. 

The  third  or  collision  bulkhead  must  be  placed  not  nearer  than 
five  feet  from  the  stem  of  the  vessel.  Iron  bulkheads  must  be 
made  not  less  than  one-quarter  of  an  inch  in  thickness,  and  wooden 
bulkheads  must  be  of  equal  strength  and  covered  with  iron  plates 
not  less  than  one-sixteenth  of  an  inch  in  thickness. 

Steam  ferry-boats  of  50  tons  burden  and  over  must  be  supplied 
with  life-boats  as  in  the  judgment  of  the  inspector  will  best  pro- 
mote the  security  of  life  on  board  of  such  vessels  in  case  of  disas- 
ter, according  to  the  average  number  of  passengers  carried  per 
trip. 

Table  of  dimensions  of  boats  for  passenger  steamers  of  100  gross 
tons  and  under,  navigating  lakes,  bays,  sounds,  and  rivers,  other 
than  the  Red  River  of  the  North  and  rivers  whose  waters  flow  into 
the  Gulf  of  Mexico.  Boats  of  other  dimensions  of  equivalent 
cubical  capacity  may  be  used  :  — 


NUMBEK   OF   Tons 

(Gross). 

12   f- 

3  < 
*5 

Dimensions. 

H 

< 

H 
'A 

o 

Length. 

Breadth. 

Depth. 

Steamers  over  : 

Ft. 

Ft.      In. 

Ft.  In. 

Cu.  Ft. 

50  and  not  over  100 

1 

18 

5       6 

2     3 

.7 

155.9 

30     "          "           50 

1 

16 

5      6 

2     3 

.  / 

138.6 

10     "         "           30 

1 

14 

5      0 

2     2 

— 

106.1 

0     "         '•            10 

1 

14 

4      (3 

2     0 

.7 

88.2 

The  cubical  capacity  of  life-boats  on  steamers  of  100  gross  tons 
and  under,  navigating  the  Red  River  of  the  North  and  rivers  whose 


Buoyancy  Apparatus  447 

waters  flow  into  the  Gulf  of  .Mexico,  shall  be  as  follows,  measured 
as  per  example  in  Section  •_'.  Rule  III:  — 

Cubic  Feet. 

Steamers  over  50  and  not  over  100  gross  tons  .  .  105 
Steamers  over  30  and  not  over  r>o  gross  tons  .  .  92 
Steamers  over  1<»  and  not  over  30  gross  tons  .  .  71 
Steamers  of  10  gross  tons  and  under 60 

The  life-boat  on  steamers  between  50 and  100  tons  must  be  in 
addition  to  the  working  boat  required  by  Section  6  of  this  rule. 

The  boat  for  passenger  steamers  of  10  tons  and  less  may  be 
dispensed  with  if  such  steamer  is  provided  with  metallic  air 
chambers,  placed  under  the  seats  and  in  the  ends  of  said  vessel,  of 
sufficient  capacity  to  float  the  inert  weight  of  said  vessel  including 
her  boilers  and  machinery ■  otherwise  the  life-boat  referred  to  in 
the  above  table  must  be  either  carried  or  towed  at  all  times  when 
being  navigated  with  passengers  on  board;  and  all  such  vessels 
referred  to  in  this  section  shall  also  be  provided  with  one  life- 
preserver  for  every  person  which  the  inspection  certificate  shall 
allow  them  to  cany,  including  officers  and  crew. 

All  open  steam  launches  or  other  steam-vessels  of  five  tons  burden 
or  less,  used  for  pleasure  purposes  only,  will  not  be  required  to  carry 
a  life-boat.  Such  steamers  when  licensed  to  carry  passengers  may 
dispense  with  the  life-boat  when  such  vessels  are  provided  with 
metallic  air  chambers  placed  under  the  seats  and  in  the  ends  of  said 
vessels,  of  sufficient  capacity  to  float  the  inert  weight  of  said 
vessel,  including  her  boilers  and  machinery  ;  and  such  vessels 
shall  also  be  provided  with  one  life-preserver  for  every  person 
which  the  inspection  certificate  shall  allow  them  to  carry,  including 
the  officers  and  crew  ;  and  every  such  steam-vessel  carrying  fifteen 
passengers  or  less  shall  carry  at  least  two  fire  buckets  and  one  axe. 

All  steam-vessels  certificated  as  ocean,  lake,  bay,  or  sound  at  their 
annual  inspection  after  the  adoption  <>f  this  ride  (except  vessels  of 
100  tons  and  under,  inspected  under  the  provisions  of  Section  4426. 
Revised  Statutes,  and  freight  and  towing  steamers,  inspected 
under  the  provisions  of  Section  4427.  Revised  Statutes)  shall  be 
provided  with  a  line-carrying  projectile  and  the*  means  of  propel- 
ling it.  such  as  may  have  received  the  formal  approval  of  the  Board 
of  Supervising  Inspectors. 

All  inland  passenger  stpamers  are  required  to  be  provided  with 
fire  buckets,  barrels,  axes,  as  follov 


448 


The   Naval   Constructor 


Gross  Tows. 

Barrels. 

Buckets. 

Axes. 

All  steamers  over  10  tons  and  not 
over  25  tons 

2 
4 
6 
8 

18 
24 

35 

50 

1 

1 

2 

2 

4 

6 

8 
10 

All  steamers  over  25  tons  and  not 
over  50  tons 

All  steamers  over  50  tons  and  not 
over  100  tons 

All   steamers  over   100  tons  and 
not  over  200  tons     .... 

All   steamers  over   200  tons  and 

All   steamers  over   500  tons  and 
All  steamers  over  1000  tons 

1 
1 
2 
4 

6 

8 

For  tug,  tow,  freight,  and  small  ferry  steamers 


Gross  Tons. 

Barrels. 

Buckets. 

Axes. 

All  steamers  over  10  tons  and  not 

2 

4 

G 

8 

12 

15 

20 

•2  5 

1 
1 

2 

2 

2 

o 
o 

4 

5 

All  steamers  over  25  tons  and  not 
All  steamers  over  50  tons  and  not 
All   steamers  over   100  tons  and 

All   steamers  over   200  tons  and 
not  over  500  tons     .... 

AH    steamers  over   500  tons  and 
not  over  1000  tons  .... 

All  steamers  over  1000  tons,  not 
less  than    ....... 

1 
1 
1 
2 
3 
4 

Provided,  however,    That  tanks  of  suitable  dimensions  and  arrange- 
ments, or  buckets  in  sufficient  number  may  be  substituted  for  barrels  on 
all  vessels.     Five  buckets  shall  be  considered  as  equivalent  to  one  barrel. 

Boilers  449 

Fire  buckets,  barrels,  or  tanks,  must  be  constantly  filled  with 
water,  and  in  such  positions  on  board  ;is  shall  be  most  convenient 
for  extinguishment  of  lire. 

All  axes  must  be  bo  Located  as  to  be  readily  found  in  time  of 
need,  must  not  be  used  for  general  purposes,  and  must  be  kept  in 
good  condition. 

All  hay,  straw,  or  baled  shavings  carried  on  deck  of  passenger 
steamers  shall  be  covered  with  a  tarpaulin  while  on  board. 

Boilers. —  All  boilers  shall  have  a  clear  space  of  at  least  8 
inches  between  the  underside  of  the  cylindrical  shell  and  the  floor 
or  keelson. 

All  boilers  shall  have  a  clear  space  at  the  back  and  ends  thereof 
of  2  feet  opposite  the  back  connection  door;  provided,  that  on 
vessels  constructed  of  iron  or  steel  with  metal  bulkheads  the  dis- 
tance between  back  connection  doors  and  such  metal  bulkheads 
shall  not  be  less  than  16  inches. 

Donkey  Boiler.  —  Every  sea-going  steamer  carrying  passen- 
gers shall  be  supplied  with  an  auxiliary  or  donkey  boiler  of  suffi- 
cient capacity  to  work  the  fire  pumps,  and  such  boiler  shall  not 
be  placed  below  the  lower  decks  except  on  single-deck  vessels. 


450  The   Naval   Constructor 

CHAPTER  V. 

INTERNATIONAL   RULES    OF   1897.* 

Preliminary  Definitions.  —  In  the  following  rules  every 
steam-vessel  which  is  under  sail  and  not  under  steam  is  to  be  con- 
sidered a  sailing-vessel,  and  every  vessel  under  steam,  whether 
under  sail  or  not,  is  to  be  considered  a  steam-vessel. 

The  word  "steam-vessel  "  shall  include  any  vessel  propelled  by 
machinery. 

A  vessel  is  "under  way"  within  the  meaning  of  these  rules 
when  she  is  not  at  anchor,  or  made  fast  to  the  shore,  or  aground. 

Lights,  etc.  — The  word  "  visible  "  in  these  rules  when  applied 
to  lights  shall  mean  visible  on  a  dark  night  with  a  clear  atmos- 
phere. 

The  rules  concerning  lights  shall  be  complied  with  in  all 
weathers  from  sunset  to  sunrise,  and  during  such  time  no  other 
lights  which  may  be  mistaken  for  the  prescribed  lights  shall  be 
exhibited. 

Steam-Vessel's  Masthead  Light.  —  A  steam-vessel,  when 
under  way,  shall  carry:  {a)  On  or  in  front  of  the  foremast,  or  if  a 
vessel  without  a  foremast,  then  in  the  fore  part  of  the  vessel,  at  a 
height  above  the  hull  of  not  less  than  twenty  feet,  and  if  the 
breadth  of  the  vessel  exceeds  twenty  feet,  at  a  height  above  the 
hull  not  less  than  such  breadth,  so,  however,  that  the  light  need 
not  be  carried  at  a  greater  height  above  the  hull  than  forty  feet, 
a  bright,  white  light,  so  constructed  as  to  show  an  unbroken  light 
over  an  arc  of  the  horizon  of  twenty  points  of  the  compass,  so 
fixed  as  to  throw  the  light  ten  points  on  each  side  of  the  vessel, 
namely,  from  right  ahead  to  two  points  abaft  the  beam  on  either 
side,  and  of  such  a  character  as  to  be  visible  at  a  distance  of  at 
least  five  miles. 

Steam-Vessel's  Side-Lights.  —  (b)  On  the  starboard  side  a 
green  light  so  constructed  as  to  show  an  unbroken  light  over  an 
arc  of  the  horizon  of  ten  points  of  the  compass,  so  fixed  as  to 
throw  the  light  from  right  ahead  to  two  points  abaft  the  beam 
on  the  starboard  side,  and  of  such  a  character  as  to  be  visible  at  a 
distance  of  at  least  two  miles. 

(c)  On  the  port  side  a  red  light  so  constructed  as  to  show  an 
unbroken  light  over  an  arc  of  the  horizon  of  ten  points  of  the 
compass,  so  fixed  as  to  throw  the  light  from  right  ahead  to  two 
*  Subscribed  to  by  tbe  Maritime  Nations. 


Side  and   Range   Lights 


451 


points  abaft  the  beam  on  the  port  side,  and  of  such  a  character  as 
to  be  visible  at  adistanee  of  at  least  two  miles. 

(d)  The  said  green  and  red  side-lights  will  be  fitted  with  in- 
board screens  projecting  at  least  three  feet  forward  from  the  light, 
so  as  to  prevent  these  lights  from  being  seen  across  the  buw. 
(Fig.  286.) 


i 
i 
i 

!§ 

IE 


o«5 


Net  less  than  36 


Fin.  286. 

Steam-Vessels'  Range  Lights.  —  (e)  A  steam-vessel  when 
under  way  may  carry  an  additional  white  light  similar  in  con- 
struction  to  the  light  mentioned  in  subdivision  (a).  These  lights 
shall  be  so  placed  in  line  with  the  keel  that  one  shall  be  at  least 
fifteen  feet  higher  than  the  other,  and  in  such  a  position  with 
reference  to  each  other  that  the  lower  light  shall  be  forward  of 
the  upper  one.  The  vertical  distance  between  these  lights  shall 
be  less  than  the  horizontal  distance. 

Steam-Vessels  when  Towing.  —  A  steam-vessel  when  tow- 
ing another  vessel  shall,  in  addition  to  her  side-lights,  carry  two 
bright  white  lights  in  a  vertical  line  one  over  the  other,  and  not 
less  than  six  feet  apart  ;  and  when  towing  more  than  one  vessel 
shall  carry  an  additional  bright  white  light  six  feet  above  or  below 
such  light,  if  the  length  of  the  tow  measuring  from  the  stern  of 
the  towing  vessel  to  the  stern  of  the  last  vessel  towed  exceeds  six 
hundred  feet.  Each  of  these  lights  shall  be  of  the  same  construc- 
tion and  character,  and  shall  be  carried  in  the  same  position  as  the 
white  light  mentioned  in  Article  2  (<t),  excepting  the  additional 
light,  which  may  be  carried  at  a  height  of  not  less  than  fourteen 
feet  above  the  hull. 

Such  steam-vessels  may  carry  a  small  white  light  abaft  the  fun- 
nel or  aftermast  for  the  vessel  towed  to  steer  by,  but  such  light 
shall  not  be  visible  forward  of  the  beam. 


452  The  Naval  Constructor 


Special  Lights.  —  (a)  A  vessel  which  from  any  accident  is  not 
under  command  shall  carry  at  the  same  height  as  the  white  light 
mentioned  in  Article  2  (a),  where  they  can  be  best  seen,  and  if 
a  steam-vessel  in  lieu  of  that  light,  two  red  lights,  in  a  vertical 
line  one  over  the  other,  not  less  than  six  feet  apart,  and  of  such  a 
character  as  to  be  visible  all  around  the  horizon  at  a  distance  of  at 
least  two  miles  ;  and  shall  by  day  carry  in  a  vertical  line  one  over 
the  other,  not  less  than  six  feet  apart,  where  they  can  be  best  seen, 
two  black  balls  or  shapes,  each  two  feet  in  diameter. 

(6)  A  vessel  employed  in  laying  or  in  picking  up  a  telegraph 
cable  shall  carry  in  the  same  position  as  the  white  light  mentioned 
in  Article  2  (a),  and  if  a  steam-vessel  in  lieu  of  that  light,  three 
lights  in  a  vertical  line  one  over  the  other,  not  less  than  six  feet 
apart.  The  highest  and  lowest  of  these  lights  shall  be  red,  and 
the  middle  light  shall  be  white,  and  they  shall  be  of  such  a  char- 
acter as  to  be  visible  all  around  the  horizon  at  a  distance  of  at 
least  two  miles.  By  day  she  shall  carry  in  a  vertical  line  one  over 
the  other,  not  less  than  six  feet  apart,  where  they  can  be  best  seen, 
three  shapes  not  less  than  two  feet  in  diameter,  of  which  the  high- 
est and  the  lowest  shall  be  globular  in  shape  and  red  in  color,  and 
the  middle  one  diamond  in  shape  and  white. 

(c)  The  vessels  referred  to  in  this  article,  when  not  making  way 
through  the  water,  shall  not  carry  the  side-lights,  but  when  mak- 
ing way  shall  carry  them. 

(d)  The  lights  and  shapes  required  to  be  shown  by  this  article 
are  to  be  taken  by  other  vessels  as  signals  that  the  vessel  showing 
them  is  not  under  command  and  cannot  therefore  get  out  of  the 
way. 

These  signals  are  not  signals  of  vessels  in  distress  and  requiring 
assistance.     Such  signals  are  contained  in  Article  31. 

Lights  for  Sailing-Vessels  and  Vessels  in  Tow.  —  A  sail- 
ing-vessel under  way  and  any  vessel  being  towed  shall  carry  the 
same  lights  as  are  prescribed  by  Article  2  for  a  steam-vessel 
under  way,  with  the  exception  of  the  white  lights  mentioned 
therein,  which  they  shall  never  carry. 

Lights  for  Small  Vessels.  —  Whenever,  as  in  the  case  of 
small  vessels  under  way  during  bad  weather,  the  green  and  red 
lights  cannot  be  fixed,  these  lights  shall  be  kept  at  hand,  lighted 
and  ready  for  use  ;  and  shall  on  the  approach  of  or  to  other 
vessels,  be  exhibited  on  their  respective  sides  in  sufficient  time  to 
prevent  collision,  in  such  manner  as  to  make  them  most  visible, 
and  so  that  the  green  light  shall  not  be  seen  on  the  port  side,  nor 
the  red  light  on  the  starboard  side,  nor,  if  practicable,  more  than 
two  points  abaft  the  beam  on  their  respective  sides.  To  make 
the  use  of  these  portable  lights  more  certain  and  easy,  the  lanterns 


Lights  for   Pilot  Vessels  453 

containing  them  shall  each  be  painted  outside  with  the  color  of 
the  light  they  respectively  contain,  and  shall  he  provided  with 
proper  screens. 

Lights  for  Small  Steam  and  Sail  Vessels  and  Open 
Boats.  —  Steam-vessels  of  less  than  forty,  and  vessels  under  oars 
or  sails  of  less  than  twenty  tons  gross  tonnage,  respectively,  and 

rowing  boats,  when  under  way.  shall  not  be  required  to  carry  the 
lights  mentioned  in  Article  2  (a),  (6),  and  (c),  but  if  they  do  not 

carry  them  they  shall  be  provided  with  the  following  lights  :  — 

First :  Steam-vessels  of  less  than  forty  tons  shall  carry  :  — 

In  the  fore  part  of  the  vessel  or  on  or  in  front  of  the  funnel, 
where  it  can  be  best  seen,  and  at  a  height  above  the  gunwale  of 
not  less  than  nine  feet,  a  bright  white  light  constructed  and  fixed 
as  prescribed  in  Article  2  (a),  and  of  such  a  character  as  to  be 
visible  at  a  distance  of  at  least  two  miles. 

(b)  Green  and  red  side-lights  constructed  and  fixed  as  pre- 
scribed in  Article  2  (6)  and  (c),  and  of  such  a  character  as  to  be 
visible  at  a  distance  of  at  least  one  mile,  or  a  combined  lantern 
showing  green  and  red  light  from  right  ahead  to  two  points  abaft 
the  beam"  on  their  respective  sides.  Such  lanterns  shall  be  car- 
ried not  less  than  three  feet  below  the  white  light. 

Second:  Small  steamboats,  such  as  are  carried  by  sea-going 
vessels,  may  carry  the  white  light  at  a  less  height  than  nine  feet 
above  the  gunwale,  but  it  shall  be  carried  above  the  combined 
light  mentioned  in  subdivision  one  (6). 

Third:  Vessels  under  oars  or  sails  of  less  than  twenty  tons 
shall  have  ready  at  hand  a  lantern  with  a  green  glass  on  one  side 
and  a  red  glass  on  the  other  side,  which,  on  the  approach  of  or  to 
other  vessels,  shall  be  exhibited  in  sufficient  time  to  prevent  col- 
lision, so  that  the  green  light  shall  not  be  seen  on  the  port  side, 
nor  the  red  light  on  the  starboard  side. 

Fourth  :  Rowing  boats,  whether  under  oars  or  sail,  shall  have 
ready  at  hand  a  lantern  showing  a  white  light  which  shall  be 
temporarily  exhibited  in  sufficient  time  to  prevent  collision. 

The  vessels  referred  to  in  this  article  shall  not  be  required  to 
carry  the  lights  prescribed  by  Article  4  (a)  and  Article  11,  last 
paragraph. 

Lights  for  Pilot  Vessels. — Pilot  vessels,  when  engaged  on 
their  station  on  pilotage  duty,  shall  not  show  the  lights  required 
for  Other  vessels,  but  shall  carry  a  white  light  at  the  masthead, 
visible  all  around  the  horizon,  and  shall  also  exhibit  a  flare-up 
light  or  flare-up  lights  at  short  intervals,  which  shall  never  exceed 
fifteen  minu1 

On  the  near  approach  of  or  to  othervessels  they  shall  have  their 
side-lights  lighted,  ready  for  use,  and  shall  flash  or  show  them  at 


454  The   Naval   Constructor 

short  intervals,  to  indicate  the  direction  in  which  they  are  head- 
ing ;  but  the  green  light  shall  not  he  shown  on  the  port  side,  nor 
the  red  light  on  the  starboard  side. 

A  pilot  vessel  of  such  a  class  as  to  be  obliged  to  go  alongside  of 
a  vessel  to  put  a  pilot  on  board,  inay  show  the  white  light  instead 
of  carrying  it  at  the  masthead,  and  may  instead  of  the  colored 
lights  above  mentioned,  have  at  hand,  ready  for  use,  a  lantern 
with  green  glass  on  one  side  and  red  glass  on  the  other,  to  be  used 
as  prescribed  above. 

Pilot  vessels,  when  not  engaged  on  their  station  on  pilotage 
duty,  shall  carry  lights  similar  to  those  of  other  vessels  of  their 
tonnage. 

A  steam  pilot  vessel  when  engaged  on  her  station  on  pilotage 
duty  and  in  the  waters  of  the  United  States,  and  not  at  anchor, 
shall,  in  addition  to  the  lights  required  for  all  pilot  boats,  carry  at 
a  distance  of  eight  feet  below  her  white  masthead  light  a  red 
light,  visible  all  around  the  horizon,  and  of  such  character  as  to  be 
visible  on  a  dark  night  with  a  clear  atmosphere  at  a  distance  of 
at  least  two  miles,  and  also  the  colored  side-lights  required  to  be 
carried  by  vessels  when  under  way. 

When  engaged  on  her  station  on  pilotage  duty  and  in  waters  of 
the  United  States,  and  at  anchor,  she  shall  carry,  in  addition  to  the 
lights  required  for  all  pilot  boats,  the  red  light  above  mentioned, 
but  not  the  colored  side-lights. 

When  not  engaged  on  her  station  on  pilotage  duty,  she  shall 
carry  the  same  lights  as  other  steam-vessels. 

Lights,  etc.,  of  Fishing  Vessels.  —  (Article  9,  act  of  August 
19,  1890,  was  repealed  by  act  of  May  28,  1894,  and  Article  10,  act 
of  March  3,  1885,  was  re-enacted  in  part  by  act  of  August  13, 
1894,  and  is  reproduced  here  in  part  as  Article  9.  It  will  be  the 
object  of  further  consideration  by  the  maritime  powers.) 

Fishing  vessels  of  less  than  twenty  tons  net  registered  tonnage, 
when  under  way  and  not  having  their  nets,  trawls,  dredges,  or 
lines  in  the  water,  shall  not  be  obliged  to  carry  the  colored  side- 
lights ;  but  every  such  vessel  shall  in  lieu  thereof  have  ready  at 
hand  a  lantern  with  a  green  glass  on  the  one  side  and  red  glass  on 
the  other  side,  and  on  approaching  to  or  being  approached  by  an- 
other vessel,  such  lanterns  shall  be  exhibited  in  sufficient  time  to 
prevent  collision,  so  that  the  green  light  shall  not  be  seen  on  the 
port  side,  nor  the  red  light  on  the  starboard  side. 

Lights  for  Fishing  Vessels  on  European   Coasts. — The 

following  portion  of  this  article  applies  only  to  fishing  vessels  and 
boats  when  in  the  sea  off  the  coast  of  Europe  lying  north  of  Cape 
Finisterre  :  — 

(a)  All  fishing  vessels  and  fishing  boats  of  twenty  tons  net  regis- 


Lights  tor  Fishing  Vessels  455 

tered  tonnage  or  upward,  when  under  way  and  when  not  having 
their  nets,  trawls,  dredges,  or  lines  in  the  water,  shall  carry  and 
show  the  same  lights  as  other  vessels  under  way. 

(&)  All  vessels  when  engaged  in  fishing  with  drift-nets  shall 
exhibit  two  white  lights  from  any  part  of  the  vessel  where  they 
can  be  best  seen.  Such  lights  shall  be  placed  so  that  the  vertical 
distance  between  them  shall  not  be  less  than  six  feet  and  more 
than  ten  feet,  and  so  that  the  horizontal  distance  between  them, 
measured  in  a  line  with  the  keel  of  the  vessel,  shall  not  be  le 
than  live  feet  and  not  more  than  ten  feet.  The  lower  of  these 
two  lights  shall  be  the  more  forward,  and  both  of  them  shall  be  of 
such  a  character  and  contained  in  lanterns  of  such  construction  as 
to  show  all  around  the  horizon,  on  a  dark  night  with  a  clear  at- 
mosphere, for  a  distance  of  not  less  than  three  miles. 

(c)  All  vessels  when  trawling,  dredging,  or  fishing  with  any  kind 
of  drag-nets,  shall  exhibit,  from  some  part  of  the  vessel  where  they 
cm  be  best  seen,  two  lights.  One  of  these  lights  shall  be  red,  and 
the  other  shall  be  white.  The  red  light  shall  be  above  the  white 
light,  and  shall  be  at  a  vertical  distance  from  it  of  not  less  than 
six  feet  and  not  more  than  twelve  feet;  and  the  horizontal  dis- 
tance between  them,  if  any,  shall  not  be  more  than  ten  feet. 
These  two  lights  shall  be  of  such  a  character  and  contained  in 
lanterns  of  such  construction  as  to  be  visible  all  around  the  hori- 
zon, on  a  dark  night  with  a  clear  atmosphere,  the  white  light  to  a 
distance  of  not  less  than  three  miles,  and  the  red  light  of  not  less 
than  two  miles. 

(d)  A  vessel  employed  in  line  fishing,  with  her  lines  out,  shall 
carry  the  same  lights  as  a  vessel  engaged  in  fishing  with  drift- 
net-. 

(e)  If  a  vessel,  when  fishing  with  a  trawl,  dredge,  or  any  kind 
of  drag-net,  becomes  stationary  in  consequence  of  her  gear  getting 
fast  to  a  rock  or  other  obstruction,  she  shall  show  the  light  and 
make  the  fog  signal  for  a  vessel  at  anchor. 

(/)  Fishing  vessels  may  at  any  time  use  a  flare-up  in  addition 
to  the  lights  which  they  are  by  this  article  required  to  carry  and 
show.  All  flare-up  lights  exhibited  by  a  vessel  when  trawling, 
dredging,  or  fishing  with  any  kind  of  drag-net,  shall  be  shown  at 
the  after-part  of  the  vessel,  excepting,  if  that  vessel  is  hanging  by 
the  stern  to  her  trawl,  dredge,  or  drag-net,  they  shall  be  exhib- 
ited fn  >m  the  bow. 

(<j)  Every  fishing  vessel,  when  at  anchor  between  sunset  and 
sunrise,  shall  exhibit  a  white  light,  visible  all  around  the  horizon 
at  a  distance  of  at  least  one  mile. 

(h)  In  a  fog  a  drift-net  vessel  attached  to  her  nets,  and  a  vessel 
when  trawling,  dredging,  or  fishing  with  any  kind  of  drag-net, 
and  a  vessel  employed  in  line  fishing  with  her  lines  out,  shall,  at 


456  The   Naval   Constructor 


intervals  of  not  more  than  two  minutes,  make  a  blast  with  her  fog- 
horn and  ring  her  bell  alternately. 

Lights  for  an  Overtaken  Vessel.  —  A  vessel  which  is  being 
overtaken  by  another  shall  .show  from  her  stern  to  such  last-men- 
tioned vessel  a  white  light  or  flare-up  light. 

The  white  light  required  to  be  shown  by  this  article  may  be 
fixed  and  carried  in  a  lantern,  but  in  such  case  the  lantern  shall 
be  so  constructed,  fitted,  and  screened  that  it  shall  throw  an  un- 
broken light  over  an  arc  of  the  horizon  of  twenty  points  of  the 
compass ;  namely,  for  six  points  from  right  aft  on  each  side  of  the 
vessel,  so  as  to  be  visible  at  a  distance  of  at  least  one  mile.  Such 
light  shall  be  carried  as  nearly  as  practicable  on  the  same  level  as 
the  side-lights. 


■■■»* 


Anchor  Lights.  — A  vessel  under  150  feet  in  length,  when  at 
anchor,  shall  carry  forward,  where  it  can  best  be  seen,  but  at  a 
height  not  exceeding  twenty  feet  above  the  hull,  a  white  light,  in 
a  lantern  so  constructed  as  to  show  a  clear,  uniform,  and  unbroken 
light  visible  all  around  the  horizon  at  a  distance  of  at  least  one 
mile. 

A  vessel  of  150  feet  or  upwards  in  length,  when  at  anchor,  shall 
carry  in  the  forward  part  of  the  vessel,  at  a  height  of  not  less  than 
twenty  feet  and  not  exceeding  forty  feet  above  the  hull,  one  such 
light,  and  at  or  near  the  stern  of  the  vessel,  and  at  such  a  height 
that  it  shall  be  not  less  than  fifteen  feet  lower  than  the  forward 
light,  another  such  light. 

The  length  of  a  vessel  shall  be  deemed  to  be  the  length  appear- 
ing in  her  certificate  of  registry. 

A  vessel  aground  in  or  near  a  fairway  shall  carry  the  above 
light  or  lights  and  the  two  red  lights  prescribed  by  Article  4  (a). 


* 


UNITED    STATES    INLAND    RULES. 

Steam-Vessels'  Masthead  Lights.  —  A  steam-vessel  when 
under  way  shall  carry  (a)  on  or  in  front  of  the  foremast,  or,  if  a 
vessel  without  a  foremast,  then  in  the  fore  part  of  the  vessel,  a 
bright  white  light  so  constructed  as  to  show  an  unbroken  light 
over  an  arc  of  the  horizon  of  twenty  points  of  the  compass,  so 
fixed  as  to  throw  the  light  ten  points  on  each  side  of  the  vessel,  — 
namely,  from  right  ahead  to  two  points  abaft  the  beam  on  either 
side,  and  of  such  a  character  as  to  be  visible  at  a  distance  of  at 
least  five  miles. 

*  For  all  vessels  navigating  harbors,  rivers  and  inland  waters  of  the 
United  States,  except  the  Great  Lakes. 


Towing   Lights  457 

Steam-Vessels'  Side-Lights.  —  (b)  On  the  starboard  side  a 
green  light  so  constructed  as  to  show  aD  unbroken  light  over  an 
arc  of  the  horizon  of  ten  points  of  the  compass,  so  tixed  as  to 
throw  the  light  from  right  ahead  to  two  points  abaft,  the  beam  on 
the  starboard  side,  and  of  such  character  as  to  be  visible  at  a  dis- 
tance of  at  least  two  miles. 

(c)  <  hi  the  port  side  a  red  light  so  constructed  as  to  show  an  un- 
broken light  over  an  are  of  the  horizon  of  ten  points  of  the  com- 
pass, so  fixed  as  to  throw  the  light  from  right  ahead  to  two  points 
abaft  the  beam  on  the  port  side,  and  of  such  a  character  as  to  be 
visible  at  a  distance  of  at  least  two  miles.     (See  Fig.  286.) 

(d)  The  saiil  green  and  red  side-lights  shall  be  fitted  with  in- 
board screens  projecting  at  least  three  feet  forward  from  the  light, 
so  as  to  prevent  these  lights  from  being  seen  across  the  bow. 

Steam-Vessels'  Range-Lights.  — (e)  A  sea-going  steam-ves- 
sel when  underway  may  carry  an  additional  white  light  similar  in 
construction  to  the  light  mentioned  in  subdivision  (a).  These  two 
lights  shall  be  so  placed  in  line  with  the  keel  that  one  shall  be  at 
least  fifteen  feet  higher  than  the  other,  and  in  such  a  position 
with  reference  to  each  other  that  the  lower  light  shall  be  forward 
of  the  upper  one.  The  vertical  distance  between  these  lights  shall 
be  less  than  the  horizontal  distance. 

(/)  All  steam  vessels  (excepting  sea-going  vessels  and  ferry- 
boats) shall  carry  in  addition  to  green  and  red  lights  required  by 
Article  2  (b)  (c),  and  screens  as  required  by  Article  2  (d),  a  central 
range  of  two  white  lights,  the  after  light  being  carried  at  an  eleva- 
tion at  least  fifteen  feet  above  the  light  at  the  head  of  the  vessel. 
The  head-light  shall  be  so  constructed  as  to  show  an  unbroken 
light  through  twenty  points  of  the  compass. — namely,  from  right 
ahead  to  two  points  abaft  the  beam  on  either  side  of  the  vessel, 
and  the  after  light  so  as  to  show  all  around  the  horizon. 

Steam- Vessels  when  Towing.  —  A  steam-vessel  when  tow- 
ing another  vessel  shall,  in  addition  to  her  side-lights,  earn'  two 
bright  white  lights  in  a  vertical  line  one  over  the  other,  not  less 
than  three  feet  apart  ;  and  when  towing  more  than  one  vessel 
shall  carry  an  additional  bright  white  light  three  feet  above  or 
below  such  lights,  if  the  length  of  the  tow  measuring  from  the 
ni  of  the  towing  vessel  to  the  stern  of  the  last  vessel  towed  ex- 
ceeds six  hundred  feet.  Each  of  these  lights  shall  be  of  the  same 
construction  and  character,  and  shall  be  carried  in  the  same  posi- 
tion as  the  white  light  mentioned  in  Article  2  (a),  or  the  after 
range-light  mentioned  in  Article  2  (/). 

Such  steam-vessels  may  carry  a  small  white  light  abaft  the  fun- 
nel or  aftermast  for  the  vessel  towed  to  steer  by,  but  such  light 
shall  not  be  visible  forward  of  the  beam. 


458  The   Naval   Constructor 


Lights  for  Sailing-Vessels  and  Vessels  in  Tow.  —  A  sail- 
ing-vessel under  way  or  being  towed  shall  carry  the  same  lights 
as  are  prescribed  by  Article  2  for  a  steam-vessel  under  way,  with 
the  exception  of  the  white  lights  mentioned  therein,  which  they 
shall  never  carry. 

Lights   for   Ferry-Boats,   Barges,    and    Canal-Boats    in 

Tow.  —  The  supervising  inspectors  of  steam-vessels  and  the 
Supervising  Inspector-General  shall  establish  such  rules  to  be 
observed  by  steam-vessels  in  passing  each  other,  and  as  to  the 
lights  to  be  carried  by  ferry-boats  and  by  barges  and  canal-boats 
when  in  tow  of  steam-vessels,  not  inconsistent  with  the  provisions 
of  this  Act,  as  they  from  time  to  time  may  deem  necessary  for 
safety,  which  rules,  when  approved  by  the  Secretary  of  Commerce 
and  Labor,  are  hereby  declared  special  rules  duly  made  by  local 
authority,  as  provided  for  in  Article  30  of  Chapter  802  of  the  Laws 
of  1890.  Two  printed  copies  of  such  rules  shall  be  furnished  to 
such  ferry-boats  and  steam-vessels,  which  rules  shall  be  kept 
posted  up  in  conspicuous  places  in  such  vessels. 

Lights  for  Small  Vessels.  —  Whenever,  as  in  the  case  of  ves- 
sels of  less  than  ten  gross  tons  under  way  during  bad  weather,  the 
green  and  red  side-lights  cannot  be  fixed,  these  lights  shall  be 
kept  at  hand,  lighted  and  ready  for  use  ;  and  shall,  on  the  ap- 
proach of  or  to  other  vessels,  be  exhibited  on  their  respective  sides 
in  sufficient  time  to  prevent  collision,  in  such  manner  as  to  make 
them  most  visible,  and  so  that  the  green  light  shall  not  be  seen  on 
the  port  side,  nor  the  red  light  on  the  starboard  side,  nor,  if  prac- 
ticable, more  than  two  points  abaft  the  beam  on  their  respective 
sides.  To  make  the  use  of  these  portable  lights  more  certain  and 
easy,  the  lanterns  containing  them  shall  each  be  painted  outside 
with  the  color  of  the  light  they  respectively  contain,  and  shall  be 
provided  with  proper  screens. 

Rowing  boats,  whether  under  oars  or  sail,  shall  have  ready  at 
hand  a  lantern  showing  a  white  light,  which  shall  be  temporarily 
exhibited  in  sufficient  time  to  prevent  collision. 

Lights  for  Pilot  Vessels.  —  Pilot  vessels,  when  engaged  on 
their  stations  on  pilotage  duty,  shall  not  show  the  lights  required 
by  other  vessels,  but  shall  carry  a  white  light  at  the  masthead, 
visible  all  around  the  horizon,  and  shall  also  exhibit  a  flare-up 
light  or  flare-up  lights  at  short  intervals,  which  shall  never  exceed 
fifteen  minutes. 

On  the  near  approach  of  or  to  other  vessels  they  shall  have 
their  side-lights  lighted,  ready  for  use,  and  shall  flash  or  show  them 
at  short  intervals,  to  indicate  the  direction  in  which  they  are  head- 


Rafts   and   Cratt   not   Provided   for       459 


ing  ;  but  the  green  light  shall  not  be  shown  on  the  port  side,  nor  the 
red  light  on  the  starboard  side. 

A  pilot  vessel  of  such  a  class  as  to  be  obliged  to  go  alongside  of 
a  vessel  to  put  a  pilot  on  board,  may  show  the  white  light  instead 
of  carrying  it  at  the  masthead,  and  may,  instead  of  the  colored  lights 
above  mentioned,  have  at  hand,  ready  for  use,  a  lantern  with  green 
glass  on  the  one  side  and  red  glass  on  the  other,  to  be  used  as  pre- 
scribed  above. 

Pilot  vessels,  when  not  engaged  on  their  station  on  pilotage 
duty,  shall  carry  lights  similar  to  those  of  other  vessels  of  their 
tonnage. 

A  steam  pilot  vessel  when  engaged  on  her  station  on  pilotage 
duty  and  in  waters  of  the  United  States,  and  not  at  anchor,  shall, 
in  addition  to  the  lights  required  for  all  pilot  boats,  carry  at  a  dis- 
tance of  eight  feet  below  her  white  masthead  light  a  red  light,  visi- 
ble all  around  the  horizon,  and  of  such  a  character  as  to  be  visible 
on  a  dark  night  with  a  clear  atmosphere  at  a  distance  of  at  least 
two  miles,  and  also  the  colored  side-lights  required  to  be  carried 
by  vessels  when  under  way. 

When  engaged  on  her  station  on  pilotage  duty  and  in  waters  of 
the  United  States,  and  at  anchor,  she  shall  carry,  in  addition  to 
the  lights  required  for  all  pilot  boats,  the  red  light  above  men- 
tioned, but  not  the  colored  side-lights. 

When  not  engaged  on  her  station  on  pilotage  duty,  she  shall 
carry  the  same  lights  as  other  steam-vessels. 

Lights,  etc.,  of  Fishing  Vessels. — Fishing  vessels  of  less 
than  ten  gross  tons,  when  under  way  and  not  having  their  nets. 
trawls,  dredges,  or  lines  in  the  water,  shall  not  be  obliged  to  carry 
the  colored  side-lights  ;  but  every  such  vessel  shall,  in  lieu  thereof, 
have  ready  at  hand  a  lantern  with  a  green  glass  on  one  side  and  a 
red  glass  on  the  other  side,  and  on  approaching  to  or  being  ap- 
proached by  another  vessel,  such  lantern  shall  be  exhibited  in  suf- 
ficient time  to  prevent  collision,  so  that  the  green  light  shall  not 
be  seen  on  the  port  side,  nor  the  red  light  on  the  starboard  side. 

All  fishing  vessels  and  fishing  boats  of  ten  gross  tons  or  upward, 
when  under  way  and  when  not  having  their  nets,  trawls,  dredges, 
or  lines  in  the  water,  shall  carry  and  show  the  same  lights  as 
other  vessels  under  way. 

All  vessels  when  trawling,  dredging,  or  fishing  with  any  kind  of 
drag-nets  or  lines,  shall  exhibit,  from  some  part  of  the  vessel 
where-  they  can  be  best  seen,  two  lights.  One  of  these  lights  shall 
be  red,  and  the  other  shall  he  white.  The  red  light  shall  be  above 
the  white  light,  and  shall  be  at  a  vertical  distance  from  it  of  not 
less  than  six  feet  and  not  more  than  twelve  feet ;  and  the  horizon- 
tal distance  between  them,  if  any,  shall  not  be  more  than  ten  feet. 


460  The   Naval   Constructor 


These  two  lights  shall  be  of  such  a  character  and  contained  in  lan- 
terns of  such  construction  as  to  be  visible  all  around  the  horizon, 
the  white  light  at  a  distance  of  not  less  than  three  miles,  and  the 
red  light  not  less  than  two  miles. 

Lights  for  Rafts,   or   Other  Craft,   not  Provided  for. — 

Rafts,  or  other  water  craft,  not  herein  provided  for,  navigating  by 
hand  power,  horse  power,  or  by  the  current  of  the  river,  shall 
carry  one  or  more  good  lights,  which  shall  be  placed  in  such  man- 
ner as  shall  be  prescribed  by  the  Board  of  Supervising  Inspectors 
of  Steam- Vessels. 

Lights  for  an  Overtaken  Vessel.  —  A  vessel  which  is  being 
overtaken  by  another,  except  a  steam-vessel  with  an  after  range- 
light  showing  all  around  the  horizon,  shall  throw  from  her  stern 
to  such  last-mentioned  vessel  a  white  or  a  flare-up  light. 

Anchor  Lights.  —  A  vessel  under  150  feet  in  length,  when  at 
anchor,  shall  carry  forward,  where  it  can  be  best  seen,  but  at  a 
height  not  exceeding  twenty  feet  above  the  hull,  a  white  light  in  a 
lantern  so  constructed  as  to  show  a  clear,  uniform,  and  unbroken 
light  visible  all  around  the  horizon  at  a  distance  of  at  least  one 
mile. 

A  vessel  of  150  feet  or  upwards  in  length,  when  at  anchor,  shall 
carry  in  the  forward  part  of  the  vessel,  at  a  height  of  not  less  than 
twenty  feet  and  not  exceeding  forty  feet  above  the  hull,  one  such 
light,  and  at  or  near  the  stern  of  the  vessel,  and  at  such  a  height 
that  it  shall  not  be  less  than  fifteen  feet  lower  than  the  forward 
light,  another  such  light. 

The  length  of  a  vessel  shall  be  deemed  to  be  the  length  appear- 
ing in  her  certificate  of  registry. 

Special  Signals.  —  Every  vessel  may,  if  necessary,  in  order  to 
attract  attention,  in  addition  to  the  lights  which  she  is  by  these 
rules  required  to  carry,  show  a  flare-up  light,  or  use  a  detonating 
signal  that  cannot  be  mistaken  for  a  distress  signal. 

Naval  Lights  and  Recognition  Signals.  —  Nothing  in  these 
rules  shall  interfere  with  the  operation  of  any  special  rules  ma.de 
by  the  Government  of  any  nation  with  respect  to  additional  sta- 
tion and  signal  lights  for  two  or  more  ships  of  war  or  for  vessels 
sailing  under  convoy,  or  with  the  exhibition  of  recognition  signals 
adopted  by  ship  owners,  which  has  been  authorized  by  their  re- 
spective Governments  and  duly  registered  and  published. 

Steam-Vessels  under  Sail  by  Day.  — A  steam-vessel  pro- 
ceeding under  sail  only,  but  having  her  funnel  up,  may  carry  in 
daytime,  forward,  where  it  can  be  best  seen,  one  black  ball  or 
shape  two  feet  in  diameter. 


Tonnage 


461 


<  I  [AFTER    VI. 


TONNAGE. 

Ton-nag k  is  a  term  used  to  define  the  hundredth  part  of  the 
cubic  capacity  of  the  combined  space  enclosed  by  the  holds  and 
erections  of  vessels  after  making  certain  restrictions  and  deduc- 
tions. When  measured  below  the  upper  deck,  i.e.,  the  internal 
capacity  of  the  boat  from  stem  to  stern,  it  is  known  as  under 
deck  tonnage  ;  when  forecastle,  poop,  bridge  house,  deck  houses, 
hatches,  etc.,  are  added  to  the  foregoing,  it  Is  called  gross  ton- 
nage, which  in  turn  becomes  the  net  register  tonnage  after 
the  legal  allowances  for  the  machinery  spaces,  crew  space,  and 
any  rooms  used  for  the  ship's  use  proper,  as  carpenter  shop, 
bo'sn's  store,  steering  gear  house,  chain  locker,  officers1  w.c's., 
etc.,  have  been  deducted. 

Tonnage  Length 


Imagin/ary  deck  lire  at  1 'a re!  the  round  of  beam  down 

t    I    I    !    I    I 


Fig.  287. 

The  rules  for  computing  tonnage,  and  the  deductions  allowed, 
are  practically  the  same  in  the  legal  enactments  of  all  the  princi- 
pal maritime  nations,  although  there  is  a  slight  difference  in  the 
amount  of  the  deduction  for  propelling  power  in  some  of  them. 

All  dimensions  should  be  measured  in  feet  and  decimals  of  a 
foot,  not  to  exceed  two  places,  unless  in  the  case  of  the  one-third 
of  the  common  interval,  when  three  decimal  places  should  be 
worked  to. 

Tonnage  Deck. —The  tonnage  deck  is  the  upper  deck  in 
all  ships  which  have  less  than  three  decks,  and  the  second  deck 
from  below  in  all  other  ships. 


462 


The  Naval   Constructor 


SPECIMEN    SCHEDULE   FOR 


Ship's  Name. 

Length,  112.75  ft.  -^  6  = 

:  18.792  ft.,  th 

e  Common  Interval  betw 

een  Areas. 

Depths  -f  4,  the  Middle  Depth  heing  Less  than  16  Ft. 

...    .... 

Area  1. 

Area  2. 

Area  3. 

Area  4. 

Area  5. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Depths. 

12.65 

12.3 

11.85 

11.4 

Common 

Interval 

3.162 

3.075 

2.962 

2.85 

between 

Breadths. 

00 

CO 

m 

CO 

oT 

co 

to 

CO 

<W  A 

.—t      ~ 

*9  0) 

H 

+3  +3 

13  0> 

O 

E3 

A    . 
t3  0> 

43 
© 

A    . 

■W  43 

13  cp 

© 

A    . 
i3  O) 

+3 

© 

3 

A    . 

+3  +3 

-73   <D 

© 
S3 

6    * 

e«  » 

t3 

eS  V 

'd 

e8  0) 

TJ 

cS  01 

"3 

cS  3) 

"3 

&  a 

<DpH 

O 

J-4 

o 
u 

o 

Pk 

o 

H 

g&H 

O 

ffl 

-^ 

CQ 

Ph 

M 

Ph 

m 

Ph 

n 

Ph 

ffl 

Ph 

1 

1 

19.35 

19.35 

20.2 

20.2 

20.4 

20.4 

20.2 

20.2 

2 

4 

18.85 

75.4 

20.4 

81.6 

20.5 

82.0 

20.35 

81.4 

3 

2 

16.65 

33.3 

20.15 

40.3 

20.25 

40.5 

20.0 

40.0 

4 

4 

11.85 

47.4 

19.6 

78.4 

19.85 

79.4 

17.8 

71.2 

5 

1 

1.85 

1.85 

3.0 

3.0 

6.35 

6.35 

6.35 

6.35 

177.3 

223.5 

228.65 

219.15 

*l  of  Com- 

1.05* 

1.03 

.99 

.95 

mon  In- 

8865 

6705 

205785 

109575 

terval 

17730 

22350 

205785 

197235 

between 
Breadths. 

186.165 

230.205 

226.363 

208.192 

Area  1. 

Area  2. 

Area  3. 

Area  4. 

Area  5. 

Schedule  for  Tonnage   Calculations      463 


TONNAGE    CALCULATIONS. 


Area  6. 


Feet. 

10.9 


•J .  -  -o 


~  -_ 
-  i 

- 
- 


19.10 
L8.65 
14.96 

8.75 
1.0 


— 

n 
- 


19.1 
74. 6 
29.9 
35.0 
1.0 


159.6 
.91 

1596 

143»'4 

1457236 
Area  6. 


Area  7. 


Feet. 


.*  — 


Cubic  Content 

VXD 

Registeb  Toms  lob. 


Area  7. 


o      ~ 


c 
fc 


3 

4 
5 
6 

7 


— 

— 

1 

A  reas 

Brought  up, 

Sq.  Ft. 

0 

4 

186.17 

2 

230.21 

4 

226.36 

o 

208.19 

4 

145.24 

1 

0 

a 


0 

744.68 
460.42 
906.44 

416.38 

580.96 

0 


3(07,$ 


TONNAGE  OF  POOP  OK  OTIIF.It 
ClX>SBI>-£N   Sr  \'  B. 


Break  of  Deck . 


Mean  Length,  32.15  Ft. 


Common  Interval  between 
Breadths.  16.075  Ft. 


£2 


i 


3 


1 

4 
1 


—  s 

r  '- 

I  '— 

- 


20.0 
18.6 

17.15 


20.0 
74.4 
17.15 


111.55 
r.  na  \  h  "f  corn,  inter. 
°",J0)  betw.  breadths. 

66930 
X3465 
55775 


597.91 

2  —  ht.  of  break 

Cu.  ft.  1,196.82  -=-100  =  11.96  r^g.  T 


3107  ..88* 
6.26 


j  J  of  common  interval 

\     between  art' 


lst'472-3 
621676 
1864728 


19455.32  -=-100 
z=  194.55  reg.  T.  under  deck. 
11.96  break  of  deck  a>  ai 


206.51  gross  tonnage. 


464 


The   Naval   Constructor 


Length  for  Tonnage.  —  The  length  at  the  tonnage  deck  in 
all  cases  of  the  usual  sheer  is  to  be  taken  on  the  upper  surface  of 
the  deck  to  the  inside  of  the  stringer  angle  bar  at  stern  and  stern, 
the  length  so  obtained  being  subdivided  into  an  equal  number  of 
parts  as  under  :  — 

Subdivision  of  Tonnage  Length  per  British  Law. 

Class     I.    Length  of  50  feet  and  under,  4  equal  parts. 
Class    II.    Length  above  50  feet  to  120  feet,  into  6  equal 

parts. 
Class  III.    Length  above  120  feet  to  180  feet,  into  8  equal 

parts. 
Class  IV.    Length    above   180   feet   to   225  feet,  into  10 

equal  parts. 
Class    V.    Length  above  225  feet  and  upwards,  into  12 

equal  parts. 


Subdivision    of    Tonnage    Length   per  American 

Law. 

Class      I.    Length   of    50  feet   and  under,  into   6   equal 

parts. 
Class    II.    Length  above  50  feet  to  100  feet,  into  8  equal 

parts. 
Class  III.    Length  above  100  feet  to  150  feet,  into  10  equal 

parts. 
Class  IV.    Length  above    150   feet   to   200   feet,  into  12 

equal  parts. 
Class    V.    Length  above  200  feet  to  250  feet,  into  14  equal 

parts. 
Class  VI.    Length  above  250  feet,  into  16  equal  parts. 

The  stations  at  these  subdivisions  are  the  points  at  which  the 
areas  are  calculated,  and  are  numbered  from  forward  aft,  the 
foremost  being  numbered  one,  making  the  last  ordinate  in  each 
case  an  odd  number. 

Depths.  —  The  depths  are  taken  at  each  point  of  division  as 
above,  from  the  under  side  of  tonnage  deck  to  the  ceiling  at  inner 
edge  of  limber  strake,  deducting  therefrom  one-third  of  the  beam- 
camber  ;  the  depths  so  taken  are  to  be  divided  into  four  equal 
parts  if  the  midship  depth  does  not  exceed  16  feet,  otherwise  into 
six  equal  parts.     (See  Fig.  287.) 

Breadths.  — These  are  measured  off  at  each  point  of  the  verti- 
cal division  of  the  depth  as  described,  to  the  inner  edge  of  the 


Marking  of  Ship  465 

side  ceiling.  In  the  case  of  vessels  having  no  ceiling  or  sparring, 
the  breadths  must  be  taken  to  the  inner  edge  of  frame-bars. 

The  lower  breadth,  when  the  vessel  has  no  horizontal  flat  or 
flo>r.  is  Limited  to  the  distance  between  the  two  limber  strakes, 
and  in  flat-floored  vessels  to  the  extent  of  the  horizontal  flatni 

Where  the  ceding  varies  in  thickness  on  the  sides,  as  in  crossing 
a  keelson  or  stringer,  or  at  dumping  pads,  the  average  thickness 
should  be  taken.     (See  Fig.  287.) 

Sections  for  Areas.  —  When  the  sections  have  been  prepared 
in  accordance  with  the  foregoing,  the  half-breadths  may  be  meas- 
ured off  and  tabulated  in  the  manner  shown  in  the  accompanying 
table,  and  integrated  by  means  of  Simpson's  first  rule  to  deter- 
mine the  under-deck  tonnage. 

The  erections,  hatches,  and  shelter-deck,  'tween  decks  (if  any), 
may  now  be  calculated  in  detail,  and  added  to  the  under-deck 
tonnage  to  obtain  the  gross. 

Engine  Room  Deduction. —  The  actual  space  enclosed  by 
the  engine  room  must  be  calculated,  and  the  percentage  it  bears  to 
the  -ross  tonnage  determined  to  enable  the  allowance  conceded 
by  law  to  be  made.  Should  this  percentage  be  over  thirteen  and 
under  twenty,  an  allowance  of  thirty-two  per  cent  may  be  de- 
ducted from  the  gross  tonnage  in  computing  the  net  register,  or 
the  tonnage  on  which  a  ship's  dues  are  usually  paid. 

Should,  however,  the  actual  engine  room  not  exceed  thirteen 
per  cent  of  the  gross  tonnage,  the  allowance  would  then  be  the 
actual  space  plus  f  of  same. 

It  should  be  noted  that  the  gross  tonnage  is  the  same  whether 
the  vessel  is  a  steamer  or  a  sailing  ship. 

Tonnage  Deductions.  —  All  spaces  which  have  been  meas- 
ured and  deducted  from  the  gross  tonnage,  as  officers'  rooms, 
crew's  forecastle,  chain-locker,  chart-house,  etc.,  must  be  properly 
marked  over  the  door  by  having  the  certification  cut  in,  and  also 
inside,  on  a  beam  or  other  conspicuous  place. 

MARKING    OF   SHIP. 

Name.  —  The  vessel's  name  must  be  marked  on  each  bow,  and 
the  name  and  port  of  registry  on  the  stern,  on  a  dark  ground,  in 
white  or  yellow  letters,  or  on  a  light  ground  in  black  letters.  The 
letter-  .should  preferably  be  black,  and  not  less  than    4  inches 

long. 

In  addition,  ships  of  American  registry  must  have  their  name 
cut  in  large  name  boards  fitted  on  each  side  of  top  of  pilot  house, 
with  letters  not  less  than  o'  inches  high. 


466  The  Naval  Constructor 

Official  Number  and  Tonnage. — The  official  number  and 
the  net  registered  tonnage  must  be  cut  in  on  the  main  beam  or  the 
'thwartship  coaming  of  main  hatch. 

Draught  Marks.  —  A  scale  of  feet  denoting  the  draught  of 
water  must  be  cut  in  on  each  side  of  the  stem  and  stern-post  from 
one  foot  below  light  line  to  about  two  feet  above  deep  load 
draught.  These  should  be  in  Roman  letters  or  ligures,  6  inches 
long,  the  lower  line  of  such  letters  or  figures  to  coincide  with  the 
draught  line  indicated.  The  figures,  after  being  cut  in,  should  be 
painted  white  or  yellow  on  a  dark  ground. 

Space  for  Seamen.  —  In  arranging  crew's  quarters,  care  must 
be  taken  that  a  minimum  capacity  of  72  cubic  feet  is  allowed  for 
each  seaman,  and  a  clear  floor  space  of  not  less  than  twelve 
square  feet. 

NEW   YORK  YACHT    CLUB   RACING   RULES. 

Rating  Formula.  —  Yachts  shall  be  rated  for  classification 
and  time  allowance  according  to  the  following  formula :  — 

. (  Length  multiplied  by  square 

Rating  measurement  =  ^4^  J      ™0}.  of  sail  fea  divided  by 

5  \/D  ^  times   cube  root  of  dis- 

l      placement. 

The  result  is  the  measurement  for  classification  and  time  allow- 
ance. 

Length.  —  The  mean  of  the  length  over  all,  exclusive  of  bul- 
warks and  rail,  and  of  the  length  on  the  load  water  plane,  both 
measurements  to  be  taken  parallel  to  the  middle  vertical  plane, 
and  at  a  distance  from  it  equal  to  one-quarter  (^)  of  the  greatest 
beam  at  the  load  water  line. 

In  case  the  width  of  the  stern  on  deck  exceeds  one-half  (J)  the 
greatest  beam  at  the  load  water  line,  the  measurement  for  the 
length  over  all  shall  be  taken  to  a  point  abaft  the  stern,  where 
the  continuation  of  the  fair  line  of  the  top  edge  of  the  plank- 
sheer  would  intersect  the  quarter  beam  line. 

Sail  Area.  —  Sail  area  to  be  obtained  as  follows,  and  the 
square  root  of  this  area  to  be  the  yJSA  in  formula  :  — 

Mainsail.  —  A.  Measured  from  the  top  of  the  boom  (under 
the  pin  for  outhaul  shackle  on  traveller,  or  clew  slide,  when 
hauled  chock  out)  to  the  gaff  under  the  pin  of  the  sheave  of  the 
topsail  sheet,  provided  the  peak  cringle  of  the  mainsail  does  not 
extend  beyond  the  pin  ;  in  the  case  of  the  yacht  having  no  top- 


Measurement  of  Sails 


467 


sail,  or  of  the  peak  cringle  extending  beyond  the  pin  of  the 
topsail-sheet  sheave,  the  measurement  to  be  taken  to  the  peak 
lacing-hole. 

B.  Perpendicular  to  A,  measured  to  underside  of  gaff  close  in 
to  the  must. 

C.  Measured  from  top  of  boom  over  the  pin  of  the  sheave  or 
outhaul  or  end  of  clew  slide  to  underside  of  gaff  close  in  to  the 
mast. 


Fig.  288. 

D.  Perpendicular  to  C,  measured  in  to  the  mast,  in  a  line  with 
the  top  of  the  boom,  or  to  tack  cringle  of  mainsail,  if  below  top 
of  boom. 

Club  Topsail. — E.  Measured  from  upper  side  of  gaff  close 
in  to  the  mast  to  pin  of  sheave  for  topsail  sheet,  or  to  lacing-hole 
in  club. 

F.  Perpendicular  to  E,  measured  to  lower  lacing-hole  in  sprit. 

G.  From  lacing-hole  to  lacing-hole  in  sprit. 

H.  Perpendicular  to  G,  measured  to  pin  of  sheave  for  topsail 
sheet  in  gaff ;  or  to  upper  lacing-hole  in  club. 

Jib  Header.  —  K.  Measured  from  top  of  gaff  close  in  to  mast 
to  pin  of  halyard  sheave  in  topmast. 

L.  Perpendicular  to  K,  measured  to  pin  of  topsail  sheet  sheave 
in  gaff  ;  or  to  upper  lacing-hole  in  club. 


468  The  Naval   Constructor 


Lugs  ail.  —  To  be  measured  as  mainsail,  except  as  follows  :  — ■ 
A.    Upper  end  measured  to  peak  lacing-hole  in  yard. 
B  and  C.    Forward  end  measured  to  lower  lacing-hole  in  yard. 
D.    Lower  end  measured  to  tack  cringle  of  mainsail,  if  below 
top  of  boom,  or  forward  of  mast. 

Headsails.  — I.  The  perpendicular  I  to  be  measured  from  the 
deck,  at  the  foreside  of  the  mast  to  where  the  line  of  the  luff  of 
the  foremost  headsail,  or  of  the  spinnaker  halyard,  as  the  case 
may  be,  when  extended,  cuts  such  perpendicular.  In  the  case  of 
a  schooner  the  perpendicular  /  shall  be  measured  upon  the  fore- 
mast, unless  she  has  a  main  spinnaker,  the  height  of  which  exceeds 
the  perpendicular  upon  the  foremast,  in  which  case  the  excess  shall 
be  added  to  the  perpendicular  I. 

J.  The  base  J  to  be  measured  from  the  foreside  of  the  mast  to 
where  the  line  of  the  luff  of  the  foremost  headsail,  when  extended, 
cuts  the  bowsprit,  other  spar,  hull,  etc.,  as  the  case  may  be.  In 
all  cases,  if  the  distance  from  the  centre  fore-and-aft  line  of  the 
mast  to  the  outer  end  of  the  spinnaker  boom  exceeds  the  distance 
from  the  foreside  of  the  mast  to  the  bowsprit  end  (where  cut  by 
the  line  of  the  luff  of  the  foremost  headsail)  the  excess  shall  be 
added  to  the  base  of  the  fore  triangle. 

In  the  case  of  a  schooner,  the  base  J  shall  be  measured  from 
the  foremast,  but  if  the  main  or  longest  spinnaker  boom  exceeds 
the  before-mentioned  distance,  the  excess  shall  be  added  to  the 
base  J. 

In  the  case  of  a  yacht  having  no  headsail,  but  carrying  a  spin- 
naker, the  area  for  headsail  shall  be  computed  from  the  length  of 
spinnaker  boom,  and  the  height  from  deck  to  where  the  line  of 
the  halyard  of  the  spinnaker  when  extended  cuts  the  mast. 

A  spinnaker  may  have  a  headstick,  or  board,  not  longer  than 
one-twentieth  the  length  of  the  spinnaker  boom,  but  not  a  foot- 
yard,  or  more  than  one  sheet,  or  any  other  contrivance  for  extend- 
ing the  sail  to  other  than  a  triangular  shape. 

In  the  case  of  a  yacht  carrying  a  square  sail,  or  square  topsail, 
or  raffee  (together  or  separately),  the  actual  area  of  the  same  shall 
be  computed  ;  and  if  such  area  exceed  the  area  of  the  fore  trian- 
gle, the  excess  shall  be  used  in  the  total  area  for  determining  the 
rating. 

Foresail  of  Schooners.  —  To  be  measured  as  mainsail,  except 
that  the  lower  end  of  A  is  to  be  taken  at  foreside  of  mainmast,  in 
a  line  with  main  boom  gooseneck. 

Directions  for  Measuring  Sails.  —  The  measurer  shall  take 
measurements  I  and  J  for  fore  triangle,  G  and  E  for  club  topsail, 
and  the  length  of  spinnaker  boom.     If  the  other  measurements 


Calculation   of  Sail   Areas  469 

are  supplied  by  the  sailmaker,  the  measurer  shall  check  them  by' 
measuring  the  following  :  — 

Boom,  —  from  lower  eud  of  A  to  lower  end  of  D. 

Gaff  or  lug  yard,  —  from  upper  end  of  A  to  forward  end  of  B. 

Club  Topsail.  —  sheet  to  outer  lacing-hole. 

In  cases  where  it  is  necessary  for  the  official  measurer  to  meas- 
ure the  sails,  he  shall  do  so  in  the  following  manner  :  Take  the 
length  of  boom  from  mast  to  pin  of  sheave  for  outhaul,  and  length 
of  gaff  from  mast  to  pin  of  topsail  sheet  sheave  or  lacing-hole,  as 
the  case  may  require  ;  then  hoist  the  sail  with  the  tack  fast  and 
set  the  peak  and  luff  up  taut,  and  let  go  the  topping  lifts  so  that 
the  weight  of  the  boom  comes  on  the  leach  of  the  sail.  With  a 
line  and  tape,  measure  the  leach  and  luff  and  the  diagonal  C.  For 
the  headsail  measure  the  height  I  and  the  distance  J,  as  provided 
for  in  the  section  dealing  with  headsail.  For  topsail  the  sail 
should  be  hoisted  and  marked  in  a  line  with  the  gaff;  then  low- 
ered and  the  other  dimensions  taken.  From  the  measurements  so 
taken  a  sail  plan  should  be  made  and  the  other  above-specified 
measurements  obtained  therefrom. 

CALCULATION    OF   SAIL    AREAS. 

Mainsail.  —  Multiply  A  by  B  and  C  by  D,  and  add  the  two 
products  together  and  divide  by  2. 

Yard  Topsail. —  Multiply  E  by  F  and  G  by  II,  and  add  the 
two  products  together  and  divide  by  2. 

Jib  Header,  —  Multiply  K  by  L  and  divide  by  2. 

Headsails.  — Multiply  I  by  J  and  divide  by  2. 

Lugsails  and  Headsails. — No  deduction  is  to  be  made  from 
Jieadsail  area  on  the  score  of  any  portion  of  the  lugsail  area  ahead 
of  the  mast. 

Sails  Bounded  by  Curved  Edges.  —  Any  increase  in  the 
area  of  sails  due  to  curved  edges,  extended  by  battens,  or  other- 
wise, beyond  the  line  between  the  points  for  measurement,  shall 
be  computed  as  follows  :  Multiply  the  base  E  by  two-thirds  of  the 
perpendicular  P. 

Displacement.  —  D.    Displacement  to  be  obtained  as  follows  : 
At  points  dividing  the  length  of  the  load  water  line  into  live 

equal  parts,  find  areas  of  immersed  cross  sections  in  square  feet ; 

from  the  areas  in  square  feet  obtained  and  load  water  line  length, 

lind  approximate  displacement  in  cubic  feet,  which  will  be  the  D 

in  formula. 


470  The  Naval  Constructor 


Limit  of  L.W.L.  —  One  half  (h)  of  any  excess  of  L.W.L.  over 
one  hundred  and  fifteen  per  cent  (115%)  of  L  shall  be  added  to  the 
rating  measurement. 

The  L.W.L.  shall  be  the  distance  in  a  straight  line  between  the 
points  farthest  forward  and  farthest  aft,  where  the  hull,  exclusive 
of  the  rudder  post,  is  intersected  by  the  surface  of  the  water  when 
the  yacht  is  afloat,  in  racing  trim. 

Limit  of  Draught.  —  Limit  of  draught  in  feet  =.133  (rating 
measurement)  +  2.66. 

Any  excess  of  draught,  exclusive  of  centre-board,  as  per  above 
formula,  shall  be  multiplied  by  five  (5)  and  added  to  the  rating 
measurement. 

The  draught  of  any  vessel,  exclusive  of  centre-board,  shall  not 
exceed  eighteen  (18)  feet. 

Limit  of  Sail  Area.  — Any  excess  of  the  square  root  of  sail 
area  over  one  hundred  and  thirty -five  per  cent  (135%)  of  I  shall 
be  added  to  the  rating  measurement. 

All  measurements  of  hull  shall  be  taken  with  only  such  persons 
on  board  as  shall  be  required  by  the  measurer. 

All  measurements  specified  may  be  certified  to  by  the  designer, 
in  a  certificate  to  be  filed  with  the  measurer  of  the  club,  but  such 
certificate  must  be  accompanied  by  drawings,  showing  the  meas- 
urements taken,  and  the  true  line  of  flotation  of  the  vessel  when 
measured  in  racing  trim,  which  measurement  and  line  of  flotation 
must  be  verified  by  the  measurer,  before  any  certificate  of  meas- 
urement shall  be  accepted  by  the  secretary. 

If  from  any  peculiarity  in  the  build  of  a  yacht,  or  other  cause, 
the  measurer  shall  be  of  opinion  that  the  rule  will  not  rate  the 
yacht  fairly,  or  that  in  any  respect  she  does  not  comply  with  the 
requirements  of  these  rules,  he  shall  report  the  circumstances  to 
the  Regatta  Committee,  who,  with  the  measurer,  after  due 
inquiry,  shall  award  such  a  certificate  of  rating  as  they  may 
consider  equitable,  and  the  measurement  shall  be  deemed  incom- 
plete until  this  has  been  done. 

CLASSIFICATION. 

Schooners.  —  Class  A.   All  over  100  feet,  rating  measurement. 

Class  B.  Not  over  100  feet  and  over  80  feet,  rating  measure- 
ment. 

Class  C.  Not  over  80  feet  and  over  64  feet,  rating  measure- 
ment. 

Class  D.  Not  over  64  feet  and  over  51  feet,  rating  measurement. 

Class  E.  Not  over  51  feet,  rating  measurement. 


Ballast,   etc.  471 

Single-masted  Vessels  and  Yawls.  —  Class  F.  All  over 
100  feet,  rating  measurement. 

Class  (V.   Not  over  100  feet  and  over  80  feet,  rating  measurement. 

Class  11.  Not  over  80  feet  and  over  04  feet,  rating  measure- 
ment. 

Class  I.  Not  over  04  feet  and  over  51  feet,  rating  measure- 
ment. 

Class  J.  Not  over  51  feet  and  over  40  feet,  rating  measure- 
ment. 

Class  K.   40  feet  and  under,  rating  measurement. 

Sails.  — Yachts  in  races  may  carry  the  following  sails  :  — 

Schooners.  —  Mainsail,  foresail,  fore  staysail,  jib,  flying-jib, 
jib-topsail,  fore  and  main  gaff  topsail,  maintopmast  staysail,  and 
spinnaker. 

Sloops  and  Cutters.  —  Mainsail,  fore  staysail,  jib,  flying- 
jib,  jib-topsail,  gaff  topsail,  and  spinnaker. 

Yawls. — Same  as  sloops  and  cutters,  with  mizen  and  mizen- 
staysail. 

Balloon  Sails. —Yachts  may  set  light  sails  over  working 
sails. 

Boats  and  Life-Buoys. — All  yachts  shall  carry  at  least  two 
serviceable  life-buoys  on  deck  ready  for  use. 

Classes  A  and  B  of  schooners,  and  F  and  G  of  single-masted 
vessels  and  yawls,  shall  carry  on  deck  a  serviceable  round-bottom 
boat,  not  less  than  14  feet  in  length  ;  and  classes  C  and  D  of 
schooners,  and  H  and  J  of  single-masted  vessels  and  yawls,  a 
boat  as  above,  not  less  than  12  feet  in  length;  and  in  classes  E  of 
schooners,  and  J  and  K  of  single-masted  vessels  and  yawls,  a 
boat  as  above,  not  less  than  10  feet  in  length.  All  boats  to  have 
oars  and  rowlocks  or  tholepins  lashed  in. 

Bulkheads.  Ballast,  etc. --Floors  must  be  left  down  and 
bulkheads  and  doors  left  standing  ;  water-tanks  kept  in  place, 
and  at  least  one  bower  anchor  and  cable  kept  on  board.  All 
yachts,  except  in  classes  A  of  schooners  and  G  of  single-masted 
vessels  and  yawls,  shall  keep  their  galley  fixtures  and  fittings  on 
board  and  in  their  proper  places.  Trimming  by  dead-weight  shall 
not  be  allowed  after  the  preparatory  signal.  Neither  ballast  nor 
water  shall  be  taken  in  or  discharged  after  9  p.m.  of  the  day 
before  a  race,  but  the  above  restriction  may  be  waived  as  to 
water,  only  by  permission. 

Crew. —  The  number  of  men  permitted  on  a  yacht  during  a 
race  shall  not  exceed  that  given  by  the  following  table  :  — 


472  The  Naval  Constructor 

Classes  A  and  F.  One  man  for  every  250  square  feet  of  sail 
area,  or  fraction  thereof. 

Classes  B,  C,  Z),  E,  G,  H,  7,  J,  and  K.  One  man  for  every 
300  square  feet  of  sail  area,  or  fraction  thereof. 

BUILDERS'   OLD    MEASUREMENT   TONNAGE. 

This  tonnage,  commonly  called  B.  O.  M.,  is  still  much  in 
vogue  with  yacht  builders,  but  obsolete  otherwise. 

(L  -  W)  x  B  x  \B 

B.O.M.  =  l 1—^. —, 

94 

where  L  is  the  length  of  vessel  measured  along  top  of  keel 
from  after  side  of  stern  post,  to  the  intersection  of  a  perpendicu- 
lar with  the  fore  part  of  stem  under  the  bowsprit,  and  B  is  the 
extreme  breadth  to  outside  of  planking,  exclusive  of  doublings. 

THAMES    MEASUREMENT   TONNAGE. 

This  rule  was  formulated  by  the  Royal  Thames  Yacht  Club, 
and  is  much  used  for  the  measurement  of  yachts. 

m™       (L~B)XBX-LB 

TM- Si —    ' 

where  L  is  the  length  measured  in  a  straight  line  at  the  deck 
from  the  fore  part  of  stem  to  the  after  part  of  stern  post,  and  B 
is  the  extreme  breadth  to  outside  of  planking. 


Sectiox  VI. 


WEIGHT  OF  A  CUBIC  FOOT  OF  SUBSTANCES. 

Name  01   Substances.  Pounds 

A. 

Acacia 14. 1 

Alder 34.6 

Aluminum,  cast 160 

Aluminum,  sheet 108 

Aluminum,  bronze 178 

Alum 107 

Antimony 417 

Anthracite  coal,  broken,  cubic  foot  averages 54 

A  ton,  loose,  occupies  40-43  cubic  feet. 

Apple  wood 40..") 

Air 0.08 

Ash  (American) 80 

Asphalte 156 

Asbestos  Board  \"  thick,  per  square  foot 65 

B. 

Barley 38 

Basalt 170 

Babbit,  white  brass 456 

Beech 43.8 

Bell,  metal 502.5 

Birch 33 

Bismuth 608 

Bitumastic  solution  per  gallon 0 

Bituminous  coal,  broken,  cubic  foot  averages      ....  49 
A  ton.  loose,  occupies  43-48  cubic  feet. 

Box  wood 62.5 

Brick,  best  pressed 150 

Brick,  common  hard 125 

Brick,  soft  inferior 100 

Brickwork,  pressed  brick 140 

Brickwork,  ordinary 112 

Brass,  common 525-530 

Brass,  wire 533 

Bronze 544 

473 


474  The   Naval   Constructor 


Name  of  Substances.  Pounds. 
C. 

Camphor 62 

Cedar,  American  red 30.8 

Cedar,  white .  23 

Cement,  hydraulic,  ground,  loose,  American 56 

Cement,  hydraulic,  ground,  loose,  English,  Portland   .     .  90 

Cement  and  sand  (3  to  1) 130 

Cement,  hydraulic,  Louisville,  bushel  =     ......  62 

Cement,  hydraulic,  Portland,    bushel  = 96 

Cement,  Roman 100 

Charcoal 183 

Cherry 42 

Chalk 183 

Chestnut 41 

Clay 119 

Clay,  in  lump,  loose 63 

Coral 168 

Cork 15.6 

Copper 554 

Coal,  bituminous,  solid 84 

Coal,  bituminous,  broken,  loose 49 

Coal,  bituminous,  heaped  bushel,  loose 74 

Coke,  loose,  of  good  coal 62 

Coke,  loose,  heaped  bushel 40 

Cypress 41 

D. 

Deals,  Riga 43 

E. 

Earth,  common  loam,  dry,  loose .  76 

Earth,  common  loam,  dry,  moderately  rammed  ....  95 

Ebony 79.4 

Elder       43.4 

Elm,  English 35 

Emery 251 

Elm,  Canada 45 

F. 

Felspar 168 

Fir  (see  Red  Pine,  etc.)       31-41 

Flagging 168 

Flint 164 

Freestone 153 


Weight  of  a  Cubic   Foot  of  Substances  475 

N'VMK   OF   SUBSTANC E8 .  POUNDS. 

G 

Granite 164 

Graphite 137 

Glass,  flint L92 

Glass,  crown 157 

Glass,  plate .     .     .  172 

Gold,  pure  cast 1,200 

Gold,  standard 1,106 

Gneiss 168 

enheart 62.5 

Gunmetal 534 

Gum  wood 37 

Gypsum 143 

Gypsum,  ground,  bushel  — 70 

H. 

Hay  (compart,  old) 8 

Hawthorn 56.8 

Hazel       53.7 

Hemlock 25 

Hornbeam 47.4 

I. 

Ice 58.7 

India-rubber 58 

Iron,  cast  (average) 450 

Iron,  wrought,  purest 485 

Iron,  wrought,  average 480 

Ironwood 71 

Ivory 114 

J. 

Jackwood , 42 

L. 

Laburnum 57.4 

Larch 31.0 

Lancewood 42.1 

Lead,  cast •  708.5 

Lead,  sheet 711.5 

Lignum-vitae 83.2 

Lime,  quick,  ground,  loose,  or  in  small  lumps     ....  53 

Lime,  quick,  ground,  loose,  thoroughly  shaken  ....  75 

Lime,  quick,  ground,  loose,  struck  bushel 66 

Limestones 168 


476 


The  Naval  Constructor 


Name  of  Substances.  Pounds 

Limestones,  loose,  in  irregular  fragments 96 

Lime,  loose,  bushel  =      .     .     .     . 70 

Lime,  well  shaken,  bushel  = 80 

Lime  wood .     „     .  35 

Linoleum,  \"  thick  (incl.  cement)  per  sq.  ft 1.5 

M. 

Mahogany,  Spanish   .............  53 

Mahogany,  Honduras 35 

Marble .' 170 

Maple 40 

Masonry,  of  granite  or  limestone,  well  dressed    ....  165 

Masonry,  of  dry  rubble,  well  scabbled 138 

Masonry,  of  sandstone,  well  dressed 144 

Mercury,  fluid        849 

Mercury,  solid 977 

Mica 183 

Mortar,  hardened 103 

Muntz  metal 511 

N, 

Nickel  (hammered)    .............  541 

Nickel  (cast)     ........     0 516 

Nitric  Acid 79.4 

O, 

Oak,  British 58 

Oak,  Riga 43 

Oak  (American,  red,  black  or  yellow)    . 45 

Oak  (American,  white) 50 

Oil  (linseed) 58 

Oil  (olive) 57 

Oil  (petroleum) 48-58 

Oil  (whale) 58 

Ore  (red  iron) „ 327 

Ore  (brown) 245 

Ore  (Clydesdale) 191 

Oregon  Pine  (Douglas  Spruce)      .........  32 

P. 

Paper  (building)  per  roll  of  400  sq.  ft.   ......     .  52 

Petroleum,  standard  refined    .          57.75 

Petroleum,  Texas 58. 

Phosphor  Bronze       537 

Pitch       69 


Weight  of  a  Cubic   Foot  of  Substances  477 

Name  of  Substances.  Pounds. 

Pitch  pine  (U.  S.  yellow  pine) 41 

Pine  (long  leafed  Georgia  yellow  pine) 38 

Platinum MM 

Plumbago 140 

,«        i  '39 

Poplar r_"- 

Pewter 7<>:j 


Quartz 163-169 

S. 

Salt,  coarse 4o 

Sana1,  of  pure  quartz,  dry,  loose   ...         ....     90-106 

Sand,  well  shaken 00-117 

Sand,  perfectly  wet 120-140 

Sandstones  (tit  for  building) 151 

Satinwood 00 

Snow,  freshly  fallen 5-12 

Snow,  moistened  and  compacted  by  rain 15-50 

Shingle 88 

Silver  (standard) 044 

Slate 178 

Spruce,  Northern 26 

Spruce,  Southern 30 

Steel 490 

Steel,  cast 493 

Sycamore 36.8 


Tallow .     .     . 59 

Tar 63 

Talc 168 

Teak  Burmese 46 

Tile,  common 113 

Tiling,  inlaid  rubber,  per  sq.  ft 2 

Tiling,  vitrified  brick,  1}  thick,  per  sq.  ft 9 

Tiling,  white,  TV  in.  thick,  per  sq.  ft 5 

Tin       .     .     . W2 

Type  metal ,;;,;; 

Trap 170 

W. 

Walnut,  black 38 

Water,  pure  rain  or  distilled,  at  00°  F 62j 


478 


The   Naval   Constructor 


Name  of  Substances.  Pounds. 

Water,  salt ..'...        64 

Wheat 48 

Willow .     .        25.3 

White  Pine  (called  yellow  pine  in  England) 24 

White  metal,  Babbitt 456 


Y. 


Yew 


50.3 


Z. 


Zinc,  rolled 


o  o 


Zinc,  cast 


a  • 


.     .     .     .      449 

.     -     .     .      437 


WEIGHT    OF    SAIL   CANVAS. 


Canvas,  No. 
Lbs.  per  Sq.  Ft. 

0 
.205 

1 
.197 

2 
.184 

3 
.171 

4 
.154 

5 
.141 

6 
.128 

7 
.113 

8 
.104 

Weight  and   Stowage  of  Oil 


479 


WEIGHT    AND    STOWAGE    OF    OIL. 

(1'ktroi.kitm.) 


Weight 

Pounds 

Cubic  Feet 

<i  \  l.l.o.NS     I'KR 

IN    POUN  DS    li  ic 

<;  v i.i. <»n. 

FEB 
Cubic  Foot. 

peb  Ton. 

Ton. 

6.60 

48.63 

46.06 

314.6 

6.55 

40.(15 

45.67 

342.0 

6.60 

49.38 

45.36 

330.  1 

6.65 

40.75 

45.02 

336.8 

6.70 

50.i;; 

44.68 

334.3 

6.75 

51 1.50 

44.36 

331.9 

6.80 

50.88 

44.03 

320  1 

6.85 

51.25 

43.71 

327.0 

6.00 

51.62 

43.30 

324.6 

6.95 

52.00 

43.07 

322.3 

7.00 

52.36 

42.78 

320.0 

7.05 

52.75 

42.46 

317.8 

7.10 

53.12 

42.17 

315.5 

7.15 

53.50 

41.87 

313.2 

7.20 

63.86 

41.59 

311.1 

7.25 

54.24 

41.30 

309.0 

7.30 

54.61 

41.01 

306.0 

7.35 

64.99 

40.73 

304.8 

7.40 

55.37 

40.46 

302.7 

7.45 

55.74 

40.19 

300.7 

7.50 

66.11 

39.92 

208.6 

7.55 

56.48 

39.66 

296.6 

7.60 

56.85 

39.40 

204.7 

7.65 

57.23 

39.14 

292.8 

7.70 

57.61 

38.88 

290.9 

7.75 

57.00 

38.63 

289.0 

7.80 

58.36 

38.39 

287.2 

7.85 

58.73 

38.14 

285.3 

7.90 

59.10 

37.90 

283.5 

7.05 

59.47 

37.66 

281.7 

8. on 

59.85 

37.42 

280.0 

480 


The   Naval   Constructor 


WHITWORTH    STANDARD    BOLTS    AND   NUTS. 
{Dimensions  are  Given  to  the  Nearest  s\-  Inch.) 


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1  6 

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15 

16 


Bolt  Head  axd  Nuts. 


Width  across 
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Weight  of  Bolts  and   Nuts 


481 


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482 


The   Naval  Constructor 


CAPACITIES  OF  TANKS  PER  FOOT 


Width 
of 

Length 

Tank. 

2" 

2' 6" 

Gal. 

3' 

3'  6" 

4' 

4'  6" 

5' 

5'  6" 

6' 

6'  6" 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

2  ft.   .    . 

29.9 

37.4 

44.88 

52.36 

59.84' 

67.32 

74.8 

82.28 

89.76 

97.24 

2  ft.  6  in. 

•  • 

46.75 

56.1 

65.45 

74.80 

84.15 

93.5 

102.85 

112.20 

121.55 

3  ft.    .     . 

67.32 

78.54 
91.63 

89.76 
104.72 

101. 
117.81 

112.2 
130.9 

123.42 
144. 

134.64 
157.08 

145.86 
170.17 

3  ft.  6  in. 

.  . 

.      . 

4  ft 

119.68 

134.64 
151.47 

149.6 
168.30 

164.56 
185.13 

179.52 
202. 

194.48 
218.79 

5  ft.    .     . 

187. 

205.7 
226.27 

224.4 
246.84 

243.1 
267.41 

6  ft 

269.28 

291.72 
316.03 

Note.  —  To  convert  to  British  gallons,  multiply  by  .83. 


Capacities  of  Tanks 


4  S3 


OF    DEPTH  (Rectangular). 


of  Tank. 

7' 

7'  6 " 

8' 

8'  6" 

9' 

9'  6" 

10' 

10'  6" 

11' 

11'  6" 

13' 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

104.72 

112.20 

119.68 

127.16 

134.64 

142.12 

149.6 

157. 

164.56 

172. 

179.52 

130.9 

140.25 

149.6 

158.95 

168.3 

177.65 

187. 

196.35 

205.7 

215.05 

224.4 

157. 

168.3 

179 .52 

190.74 

202. 

213.18 

224.4 

235.62 

246.84 

258.06 

269.28 

183.26 

196.35 

209.44 

222.53 

235.62 

248.71 

261.8 

274.89 

288. 

301.07 

314.16 

209.44 

224.4 

239.36 

254.32 

269.28 

299.2 

314.16 

329.12 

344.08 

359. 

374. 

235.62 

252.45 

269.28 

286.11 

303. 

319.77 

336.6 

353.43 

370.26 

387.09 

404. 

261.8 

280.5 

299.2 

317.9 

336.6 

355.3 

374. 

392.7 

411.4 

430.1 

448.8 

288. 

308.55 

329.12 

349.7 

370.26 

390.83 

411.4 

332. 

452.54 

473.11 

493.68 

314.16 

336.6 

359.04 

381.48 

403.92 

426.36 

448.80 

471.24 

493.68 

516.12 

538.56 

340.34 

364.65 

388.96 

413.27 

437.58 

461 .89 

486.2 

510.51 

534.82 

559.13 

583.44 

366.52 

392.70 

418.88 

445.06 

471.24 

497.42 

523.6 

549.78 

575.96 

602.14 

628.32 

.  .  . 

120.75 

476.85 

405.9 

532.95 

561. 

589.05 

617.1 

645.15 

673.2 

.  .  . 

.  .  . 

478.72 

508.64 

538.56 

568.48 

598.4 

628.32 

658.24 

688.16 

718.08 

.  .  . 

.  .  . 

.  .  . 

540.43 

572 .22 

604.01 

635.80 

667.59 

699.38 

731.17 

762.96 

605.88 

639.54 

673.2 

706.86 

740.52 

774. IS 

807.84 

•  • 

.  .  . 

675.07 

710.6 
748. 

746.13 
785.4 

781.66 

822.8 

817.19 
860.2 

852.72 
897.6 

Weight  of  a  U.S.  gallon =8$  lbs.     Weight  of  a  British  gallou,  F.W.  =  10  lbs. 


484 


The   Naval   Constructor 


CONTENTS  OF  TANKS  PER  FOOT  OF  DEPTH 

(Cylindrical). 


DlAM. 

U.S. 
Gallons. 

DlAM. 

U.S. 
Gallons. 

DlAM. 

U.S. 
Gallons. 

Ft.    In. 

1  Foot  in 
Depth. 

Ft.   In. 

1  Foot  in 
Depth. 

Ft.    In. 

1  Foot  in 
Depth. 

1     0 

5.87 

11    0 

710.68 

21    0 

2,530.22 

1     3 

a.i" 

11    3 

743.36 

21    3 

2,652.25 

1     6 

13.21 

11     6 

776.77 

21     6 

2,715.04 

1     9 

17.88 

11    3 

810.81 

21    8 

2,778.54 

2     0 

23.43 

12    0 

S48.18 

22    0 

2,842.73 

2     3 

23.73 

12    3 

881.33 

22    3 

2,307.76 

2     6 

36.70 

12    6 

317.73 

22    6 

2,873.48 

2     9 

44.41 

12    3 

354.81 

22    8 

3,033.82 

3     0 

52.86 

13    0 

332.62 

23    0 

3,107.10 

3     3 

62.03 

13    3 

1,031.17 

23    3 

3,175.01 

3     6 

73.15 

13    6 

1.070.45 

23    6 

3,243.65 

3     9 

82.58 

13    3 

1,108.06 

23    8 

3,313.04 

4     0 

93.97 

14    0 

1,151.21 

24    0 

3,383.15 

4     3 

103.03 

14    3 

1,132.68 

24    3 

3,454.00 

4     6 

118.93 

14    6 

1,234.31 

24    6 

3,525.58 

4     9 

132.52 

14    3 

1,277.86 

24    8 

3,537.30 

5     0 

146.83 

15    0 

1,321.54 

25    0 

3,670.35 

5     3 

161.88 

15    3 

1.365.36 

25    3 

3,744.74 

5     6 

117.67 

15    6 

1,407.51 

25     6 

3,813.26 

5     9 

194.13 

15    8 

1,457.00 

25    8 

3,884.52 

6     0 

211.44 

16    0 

1,503.62 

26    0 

3,370.50 

6     3 

223.43 

16    3 

1,550.37 

26    3 

4,047.23 

6     6 

248.15 

16    6 

1,588.06 

26    6 

4,124.68 

6     9 

267.61 

16    8 

1,647.83 

26    8 

4,202.36 

7     0 

287.80 

17    0 

1.687.45 

27    0 

4,281.80 

7     3 

308.72 

17    3 

1,747.74 

27    3 

4,361.46 

7     G 

330.38 

17    6 

1,788.76 

27    6 

4,441.86 

7    a 

352.76 

17    8 

1,850.53 

27    3 

4,522.88 

8     0 

375.30 

18    0 

1,903.02 

28    0 

4,604.85 

8     3 

333.76 

18    3 

1,856.25 

28    3 

4,686.48 

8     6 

424.36 

18    6 

2,010.21 

28    6 

4,770.77 

8    a 

443.21 

18    8 

2,064.81 

28    3 

4,854.84 

a    o. 

475.75 

13    0 

2,120.34 

28    0 

4,333.64 

a    3 

502.55 

13    3 

2,176.51 

23    3 

5,025.17 

a    e 

530.08 

13    6 

2,233.23 

23    6 

5,111.44 

a    a 

558.35 

13    8 

2,231.04 

23    3 

5,138.44 

10     0 

587.35 

20    0 

2,348.41 

30    0 

5,286.18 

10     3 

617.08 

20    3 

2,408.51 

30    3 

5,374.65 

10     6 

647.55 

20    6 

2,468.35 

30    6 

5,463.85 

10   a 

678.27 

20    8 

2,528.82 

30    3 

5,553.73 

Note.  —  To  convert  to  British  gallons,  x  -83. 


Pressure   of  Water  at    \  arious    Heads       485 


PRESSURE    OF    WATER    AT    VARIOUS    HEADS. 


Formula  : 


P=  IP  x  .4334=  Pounds. 
y»_  j{,  y  ,0304  =  Kilos. 


Pressure, 

Si 

Pressure, 

~-' 

Pressi  re, 

_       -» 

*.     — 

—  -  — 

-    - 

I'- 

IN 

— 

-  -  :- 

P, 

IX 

_     >> 
—      *s 

«    lb  ™ 

p, 

IB 

Pounds 

Ki     - 

Pounds 

Kilos 

Pounds 

Kilos 

per 

per 

► 

per 

per 

►>. 

per 

per 

Sq.  In. 

Sq.  Cm. 

Sq.  In. 

Sq.  Cm. 

K 

Sq.  In. 

Sq.  Cm. 

lin. 

.03G0S 

.002537 

27  ft. 

11.691 

.82196 

64  ft. 

27.712 

L94836 

a 

.(17216 

.005074 

28 

12.124 

.85240 

65 

28.145 

1.97880 

3 

.10824 

.007611 

29 

12.557 

.88284 

66 

28.578 

2.00925 

4 

.14432 

.010148 

30 

12.990 

.91329 

67 

29.011 

2.03969 

5 

.18040 

.012685 

31 

13.423 

.94373 

68 

29.444 

2.07013 

6 

51648 

.015222 

32 

13.856 

.97417 

69    . 

29.877 

2.10057 

i 

.25256 

.01 7759 

33 

14.289 

1.00462 

70 

30.310 

2.13102 

8 

28864 

.020296 

34 

14.722 

1.03406 

71 

30.743 

2.16146 

9 

.32472 

.022S33 

35 

15.155 

1.06450 

72 

31.176 

2.19190 

10 

.36080 

.025370 

36 

15.588 

1.094:  '5 

73 

31.609 

2.22235 

11 

.39688 

.027907 

37 

16.021 

1.12S 

74 

32.042 

2.25279 

1ft. 

.433 

.030443 

38 

16.454 

1.15583 

75 

32.475 

2.28323 

■> 

.866 

.060886 

39 

16.887 

1.18627 

76 

32.908 

2.31368 

3 

1.299 

.091329 

40 

17.320 

1.21773 

77 

33.341 

2.34412 

4 

1.732 

.121773 

41 

17.753 

1.24S17 

78 

33.774 

2.37456 

5 

2.165 

.152216 

42 

18.186 

1.27861 

79 

34.207 

2.40500 

6 

2.5  98 

.182659. 

43 

18.619 

1.30906 

80 

34.640 

2.43545 

" 

3.031 

.213102 

44 

19.052 

1.33950 

81 

35.073 

2.4(3589 

8 

3.464 

.243545 

45 

19.485 

1.36994 

82 

35.506 

2.49633 

9 

3.897 

.273989 

46 

19.918 

1.40039 

83 

35.939 

2.52678 

in 

4. 330 

lO'/rtO 

47 

20.351 

1.43083 

84 

36.372 

-'.5.5722 

11 

4.763 

.33487 

48 

20.784 

1.46127 

85 

36.805 

2.58766 

12 

5.196 

.36531 

49 

21.217 

1.49171 

86 

37.238 

2.61811 

13 

5.629 

.39576 

50 

21.650 

1.52216 

87 

37.671 

2.64855 

14 

6.062 

.42620 

51 

22.083 

1.55260 

88 

38.104 

2.67- 

15 

6.495 

.45664 

52 

22.516 

1.58304 

89 

38.537 

2.709 ;:; 

it; 

6.928 

.48709 

53 

22.949 

1.61349 

90 

.  70 

2.73989 

17 

7.361 

.5175.; 

54 

23.382 

1.64393 

91 

(03 

2.77033 

18 

7.794 

.54797 

55 

23.815 

1.67437 

92 

39.836 

2.80077 

19 

8.227 

£7841 

56 

24.2  is 

1.704-2 

93 

40.269 

2.83122 

20 

8.660 

- 

57 

24.681 

1.73526 

94 

40.702 

2.86166 

21 

9.093 

.63930 

58 

25.114 

1.76570 

95 

41.135 

210 

2-2 

9.526 

.66974 

59 

25.5.57 

1.79614 

96 

41.568 

2.92255 

23 

9.959 

.70019 

60 

25.980 

1.82659 

97 

42.001 

255299 

24 

10.392 

.73063 

61 

26.413 

1.85703 

98 

42.434 

2.9S343 

•-'.'. 

10.825 

.70107 

62 

26.846 

1.88747 

99 

42.867 

351387 

26 

11.258 

.79152 

63 

27579 

1.91792 

100 

43.300 

3.04432 

The  above  table  is  calculated  for  fresh  water  :tt  a  temperature  of  G 


486 


The  Naval  Constructor 


WATER    NOTES. 


1  United  Slates  gallon 

1  United  States  gallon 

1  United  States  gallon 

1  United  States  gallon 

1  British  gallon 

1  British  gallon 

1  British  gallon 

1  British  gallon 

1  cubic  foot  of  sea  water 

1  cubic  inch  of  sea  water 

1  cubic  foot  of  fresh  water     w 

1  cubic  inch  of  fresh  water 

1  ton  of  sea  water 

1  ton  of  fresh  water 

Weight  of  fresh  water 

1  cubic  foot  of  fresh  water 

1  cubic  foot  of  fresh  water 

1  cubic  foot  of  fresh  water 

1  litre  of  fresh  water 

1  litre  of  fresh  water 

1  litre  of  fresh  water 

1  litre  of  fresh  water 

Head  of  water  in  feet  x  .4334 

Head  of  water  in  feet  x  .0304 


231  cubic  inches. 

.83  British  gallon. 

3.8  litres. 

8}  pounds  fresh  water. 

277.274  cubic  inches. 

1.205  United  States  gallons. 

4.543  litres. 

10  pounds  fresh  water. 

64.05  pounds  =  .0286  ton. 

.037,035  pounds. 

62.39  pounds  =  .0279  ton. 

.0361  pound. 

34.973  cubic  feet. 

35.905  cubic  feet. 

weight  of  salt  water  x  .974. 

7.476  United  States  gallons. 

6.232  British  gallons". 

28.375  litres. 

.264  United  States  gallon. 

.22  British  gallon. 

61.0  cubic  inches. 

.0353  cubic  foot. 

Pressure  in  lbs.  per  sq.  in. 

Pressure  in  kilos  per  sq.  cm. 


AREAS    OF   CIRCLES. 


Diam- 

Area. 

Circum- 

Diam- 

Area. 

Circum- 

eter. 

ference. 

eter. 

ference. 

i 

.000767 

.09817 

17 
32 

.22166 

1.6690 

1 
16 

.003068 

.19635 

9 
IS 

.24S50 

1.7671 

3 
35 

.006903 

.29452 

19 
32 

.27688 

1.8653 

1 

8 

.012272 

.39270 

f 

.30680 

1.9635 

h 

.019175 

.49087 

2  1 

3  2 

.33824 

2.0617 

3 

IS 

.027612 

.58905 

1  1 

IB 

.37122 

2.1598 

& 

.037583 

.68722 

23 
32 

.40574 

2.2580 

i 

.049087 

.78540 

1 

.44179 

2.3562 

A 

.062126 

.88357 

25 

3  2 

.47937 

2.4544 

6 

IS 

.076699 

.98175 

1  3 
16 

.51849 

2.5525 

11 

32 

.092806 

1.0799 

27 
32 

.55914 

2.G507 

a 

f 

.11045 

1.1781 

.60132 

2.7489 

13 
32 

.12962 

1.2763 

29 
32 

.64504 

2.8471 

h 

.15033 

1.3744 

]  r, 
16 

.69029 

2.9452 

1  5 
32" 

.17257 

1.4726 

3  1 
3  2 

.73708 

3.0434 

h 

.19635 

1.5708 

1 

.78540 

3.1416 

Areas  of  Circles 


487 


AREAS    OF    CIRCLES 


And  Lengths  of  the  Sides  of  Squares  of  the 

Same  Area. 

D  ini.  x  .8862  =  Side  of  Square. 


< 

< 

*■« 

- ■   _    X 

o 

BO 

-  s  ft 

~  _:  — 

"   -    -•- 

Z  -  7. 

■7  -  5 

*-  — 

■  ~  2 

-/  /: 

-7.±~ 

E3 

_•  g  ■;. 

o 

-  —  '• 

u  -  — 
--  • 

-.;  s  3 
~  Son 

:'-  -   . 
z  s   . 

—    ^9 

W  -  50 
-  /.  ft 

—        * 

3  ■-  * 

-i- 

o 

5:- 

•/.  a  * 

m     '  p— i 
Z  »     . 

■'-  ~-  7 

-  -•  50 

-  /.  ft 

00  §" 

1 

.785 

.89 

21 

346.36 

18.61 

41 

1,320.26 

36.34 

H 

1.767 

1.33 

21* 

363.05 

19.05 

41* 

1,352.66 

36.78 

2 

3.142 

1.77 

2'' 

380.13 

19.50 

42 

1,385.45 

37.22 

-: 

4.909 

2.22 

22* 

397.61 

19.D4 

42* 

1,4  IS.  63 

37.66 

3 

7.069 

5!gg 

23 

415.48 

20.38 

4:; 

1,452.20 

38.11 

3* 

9.621 

3.10 

•_>;  A 

4:;::.  74 

20.83 

43* 

1,486.17 

38.55 

4 

12.566 

3.54 

24 

452.39 

21.27 

44 

1 .520.53 

38.99 

4* 

15.904 

3.99 

24.V 

471.44 

21.71 

444 

1.555.29 

39.44 

5" 

19.635 

4.43 

25 

4:i0.88 

22.16 

45 

1.51  mi.  4:; 

39.88 

5* 

j:;.758 

4.87 

25* 

510.71 

22.60 

454 

1,625.97 

40.32 

6 

28.274 

5.32 

26 

530.93 

23.04 

46 

1,661.91 

40.77 

6i 

33.183 

5.76 

26* 

551.55 

23.49 

46* 

1,698.23 

41.21 

7 

38.4S5 

6.20 

27 

572.56 

23.93 

47" 

1,734.95 

41.65 

7^ 

44.17!) 

6.65 

27* 

593.96 

24.37 

47* 

1,772.06 

42.10 

8 

60.266 

7.09 

28 

615.75 

24.81 

48 

1,809.56 

42.58 

- 

56.74." 

7.. 53 

637.1 '4 

25.26 

48* 

1,847.46 

42.98 

9" 

63.617 

7. Its 

29 

660.52 

25.70 

49 

1,885.75 

43.43 

9.1 

70.882 

8.42 

29* 

683.49 

26.14 

49* 

1,924.43 

43.87 

10" 

78.540 

8.86 

30 

706.86 

26.59 

50 

1,963.50 

4-1.31 

10* 

86.590 

9.30 

:;n.! 

730.62 

27.03 

50* 

2,002.97 

44.75 

11 

'.'5.03 

9.75 

31 

754.77 

27.47 

51 

2,042.83 

45.20 

111 

103.87 

10.19 

31* 

779.31 

27.92 

51* 

2,083.08 

45.64 

12 

113.10 

10.63 

32 

804.25 

28.36 

52 

2,123.72 

46.08 

12* 

122.72 

11.08 

32* 

829.58 

28.80 

52.V 

2,164.76 

46.53 

13 

132.73 

11.52 

33 

855.30 

29.25 

53 

2,206.19 

46.:  17 

143.14 

11.96 

33* 

881.41 

29.69 

53* 

2.248.01 

47.41 

14 

153.!  4 

12.41 

34 

907.92 

30.13 

54" 

2.290.23 

47.86 

14* 

KU5.13 

12.85 

34* 

934.82 

30.57 

tnT 

2,332.83 

48.30 

15 

176.72 

13.29 

35 

962.11 

31.02 

55" 

2,375.83 

48.74 

15$ 

188.69 

13.74 

35* 

989.80 

31.46 

55* 

2,419.23 

49.19 

16 

201 .06 

14.18 

36 

1.H17.88 

31.90 

56 

2,463.01 

49.63 

i»;.v 

213.83 

14.62 

36* 

1,046.35 

32.35 

56* 

2,507.19 

50.07 

17 

226.98 

15.07 

37 

1.075. 21 

32.79 

57 

2.551.76 

50.51 

17', 

240. 

15.51 

1.104.47 

33.23 

574 

2.596.73 

50.96 

18 

254.47 

15.95 

1,134.12 

33.68 

58" 

2,642.09 

51.4(1 

J.80 

16.40 

38* 

1,164.16 

34.12 

58j 

2,687.84 

51 .84 

19 

16.84 

39 

1,194.59 

34.56 

59 

2,733.98 

52.29 

I:*' 

298.65 

17.28 

39* 

1,225.42 

35.ol 

59* 

2,780.51 

52.73 

20 

314.16 

17.72 

40 

1 ,256.64 

35.45 

60 

2,827.74 

53.17 

20J 

330.06 

18.17 

40.} 

1,288.25 

35.89 

60* 

1.76 

53.62 

488 


The   Naval   Constructor 


SPEED    TABLES. 

(Based  on  the  Admiralty  Knot  of  6,080  Fed*) 


1  Knot 

in    = 
Min.  Sec. 

Admi- 

RALTY 

Knots 
PerHr. 

1  Knot 

in    = 
Min.  Sec. 

A  mil- 
ls ALT  Y 
Knots 
Per  Hr. 

1  Knot 
in   = 
Min.  Sec. 

Admi- 
ralty 
Knots 
Per  Hr. 

1  Knot 

IN      = 
Min.  Sec. 

Admi- 
ralty 
Knots 
Per  Hr. 

1    30 

1     30.2 
1     30.4 
1     30.6 
1     30.8 

40.000 
39.911 
39.823 
39.735 
39.647 

1 
1 
1 
1 
1 

38 

38.2 

38.4 

38.6 

38.8 

36.734 
36.659 
36.585 
36.511 
36.437 

1 
1 

1 
1 
1 

46 

46.2 
46.4 
46.6 
46.8 

33.962 
33.898 
33.834 
33.771 
33.707 

1 
1 
1 
1 
1 

54 

54.2 

54.4 

54.6 

54.8 

31.578 
31.523 
31.468 
31.413 
31.358 

1     31 
1     31.2 
1     31.4 
1     31.6 
1     31.8 

39.560 
39.473 
39.387 
39.301 
39.215 

1 
1 
1 
1 
1 

39 

39.2 

39.4 

39.6 

39.8 

36.363 
36.290 
36.217 
36.144 
36.072 

1 

1 
1 
1 
1 

47 
47.2 
47.4 
47.6 

47.8 

33.644 
33.581 
33.519 
33.457 
33.395 

1 
1 

1 
1 
1 

55 

55.2 

55.4 

55.6 

55.8 

31.304 
31.250 
31.195 
31.141 
31.088 

1    32 
1    32.2 
1    32.4 
1    32.6 
1    32.8 

39.130 

39.045 
3S.961 
38.876 
38.793 

1 
1 
1 
1 
1 

40 

40.2 

40.4 

40.6 

40.8 

36.000 
35.928 
35.856 
35.785 
35.714 

1 
1 
1 
1 
1 

48 

48.2 
48.4 
48.6 
48.8 

33.333 
33.271 
33.210 
33.149 
33.088 

1 
1 
1 
1 
1 

56 
56.2 
56. 4 
56.6 
56.8 

31.034 
30.981 
30.927 
30.874 
30.821 

1    33 
1    33.2 
1    33.4 
1    33.6 
1    33.8 

38.710 

38.626 
38.543 
38.461 
38.379 

1 
1 
1 
1 
1 

41 

41.2 
41.4 
41.6 

41.8 

35.643 
35.573 
35.503 
35.433 
35.363 

1 
1 
1 
1 

1 

49 

49.2 

49.4 

49.6 

49.8 

33.027 
32.966 
32.906 
32.846 
32.786 

1 
1 
1 
1 
1 

57 
57.2 
57.4 
57.6 

57.8 

30.768 
30.716 
30.664 
30.612 
30.560 

1    34 
1    34.2 
1    34.4 
1    34.6 
1    34.S 

38.300 
38.216 
38.135 
38.054 
37.974 

1 
1 
1 
1 
1 

42 

42.2 

42.6 

42.8 

35.294 
35.225 
35.156 
35.087 
35.019 

1 
1 
1 
1 
1 

50 

50.2 
50.4 
50.6 
50.8 

32.727 
32.66S 
32.608 
32.549 
32.490 

1 
1 
1 
1 
1 

58 

58.2 
58.4 
58.6 
58.8 

30.508 
30.456 
30.405 
30.354 
30.303 

1    35 
1    35.2 
1    35.4 
1    35.6 
1    35.8 

37.894 
37.815 
37.736 
37.657 
37.578 

1 
1 
1 
1 

1 

43 

43.2 

43.4 

43.6 

43.8 

34.951 
34.883 
34.816 
34.749 
34.682 

1 
1 
1 
1 
1 

51 

51.2 

51.4 

51.6 

51.8 

32.432 
32.365 
32.315 
32.258 
32.200 

1 
1 
1 
1 

1 

59 

59.2 
59.4 
59.6 
59.8 

30.252 
30.201 
30.150 
30.100 
30.050 

1     36 
1     36.2 
1     36.4 
1    36.6 
1     36.8 

37.500 
37.422 
37.344 
37.267 
37.190 

1 
1 
1 
1 
1 

44 

44.2 

44.4 

44.6 

44.8 

34.614 
34.548 
34.482 
34.416 
34.351 

1 
1 
1 
1 
■1 

52 

52.2 

52.4 

52.6 

52.8 

32.142 
32.085 
32.028 
31.971 
31.914 

2 
2 
2 
2 

2 

0 

0.2 

0.4 

0.6 

0.8 

30.000 
29.950 
29.900 
29.850 
29.801 

1     37 
1    37.2 
1    37.4 
1    37.6 
1    37.8 

37.113 
37.037 
36.961 
36.885 
36.809 

1 
1 
1 

1 
1 

45 

45.2 

45.4 

45.6 

45.8 

34.285 
34.220 
34.155 
34.090 
34.026 

1 
1 
1 
1 
1 

53 

53.2 
53.4 
53.6 
53.8 

31.858 
31.802 
31.746 
31.690 
31.634 

2 
2 
2 
2 
2 

1 

1.2 

1.4 

1.6 

1.8 

29.752 
29.702 
29.654 
29.605 
29.556 

*  The  knot,  or  nautical  mile,  is  actually  6,082.66  feet. 
The  statute,  or  land,  mile  is  5,280  feet. 


Speed  Tables 


489 


SPEED    TABLES.—  (Continued.) 


1  Knot 

IN     = 

Min.  Sec 

Admi- 

B  \I.TY 
BJNOT8 

Per  Hr. 

1  Knot 

IN      = 

Min.  Sec. 

Admi- 
ralty 

'   K  M>  IS 

Per  Hr. 

1  Kn.>t 
in    = 
Min.  Sec 

Al'MI- 

i:  MiTI 

Kn.i  I  - 
Per  Hr. 

1  Knot 

in     = 
Min.  Sec. 

A  DMI- 

KA  1.1V 

Knoi  s 
Pel  Hr. 

2      2 

2      2  2 

2      ••  4 

2     25 

2      2.8 

29.508 
29.459 
29.411 
29.363 
29.315 

•> 

•_> 
2 
o 
■  ) 

11 

11.2 

11.4 

11.6 

11.8 

27.4S0 
27.438 
27.396 
27.355 

27.314 

2 

2 

2 
•  > 

20 
2H.2 
20.4 
20.6 

20.8 

25.714 

25.677 
25.641 
25.604 

o 

o 

•  > 

•  > 

2 

29 
2: 12 
2V4 
29.6 
29.8 

24.161 
24.128 
24.096 
24.064 
24.032 

2      3 
2      3.2 

2     ;;  i 

2      3.6 
2      3.8 

29.268 
29.220 
173 
29.126 
29.079 

2 

•  > 

2 

•  » 

12 
12.2 

12.4 
12.6 

12.8 

''7.272 
27531 
27.190 
27.149 
27.108 

2 
•> 

2 

•  > 

•  > 

21 

"1 ." 
21.4 
21.6 
21.8 

25.532 
25.495 

25.45:  i 
25.423 
25581 

2 
2 
2 

o 

•> 

30 

302 

30.4 

30.6 

30.8 

24.000 
23.968 
23.936 
23.904 
23..S72 

2      4 
2       4.2 
2      4.4 
2      4.6 
2      4.8 

29.032 
28585 
28.9  - 
28.892 

•> 
2 

•  > 
— 

2 

•> 

13 
13.2 

13.4 
13.6 

13.8 

27.066 
27.026 
26.986 
26.946 
26.905 

■  > 
•  > 
2 

■  > 
2 

22 

22.2 
22!  4 
22.6 
22.8 

25.352 
25516 

'J5.-J-M 

25.245 

25.210 

2 
2 
2 

2 

31 
31.2 
31.4 
31.6 

31.8 

23.Mii 
23.809 
23.778 
23.746 
23.715 

2      5 
2      5.2 
2      5.4 
2      5.6 
2      5.S 

28.800 
28.753 
28.708 
28.662 
28.616 

2 
2 
2 

■  • 
•  > 

14 

14.2 

14.4 

14.6 

14.8 

26.864 
26.825 
26.785 

2.'.. 745 
26.705 

o 
2 
2 

o 

o 

23 

2:;. 2 

23.4 

23.6 

-23.8 

25.174 
25.139 
25.104 
25.069 

25.034 

2 

•  > 

•  > 
2 
o 

32 

32.2 

32.4 

32.6 
32.8 

23.684 
23.653 
23.622 
23.591 

23.560 

2      6 
2      6.2 
2      0.4 
2      6.6 
2      6.8 

.70 
28.526 
28.481 

136 
J-.391 

•  > 
2 
•> 

•  > 

15 

15.2 

15.4 

15.6 

15.8 

26.666 
26.627 
26.687 

26509 

2 

o 
2 

2 

o 

24 

24.2 
24.4 
•24  6 
24. S 

25.000 

24.965 

245 

24.* 

24561 

o 

•  I 

•  ) 
2 

Q 

33 
33.2 

33.4 
33.6 
33.8 

23.529 
23.498 

23.468 

23.437 
23.407 

2      7 
'_'      7.2 
2      7.4 
2      7.6 
2      7.8 

28.346 
28.301 
28.257 
28.213 

28.169 

•  > 

•  > 

•  > 

•  > 

16 
16.2 

16.4 
16.6 

16.8 

26.470 

26. 431 

26.392 

354 

26.315 

•  > 
■  ■ 
2 
2 
2 

25 
25.2 
25.4 
25.6 

24527 

24.793 

24.759 
24.725 
24.691 

2 

2 
2 
2 

•  > 

34 
34.2 

34.4 
34.6 

34.8 

23.376 

'_':;. 334 
23.316 

23.-. 
23.255 

2      8 
2      8.2 
2      8.4 
2      8.6 
2      8.8 

28.12(1 
28.081 
28.037 
27.993 

27.950 

•  > 

•  > 
2 
2 

•  » 

17 
17.2 

17.4 

17..; 

17.8 

26.278 

26.2 

26.200 

26.162 

26.124 

o 
2 
2 

2 

2 

26 

26.2 

•_v,.4 

2>:..; 

26.8 

24.657 
24.623 

24.5:  mi 
24.556 
24.523 

2 
2 

2 
2 

35 

35.2 

35.4 

35.6 

35.8 

23.2-5 
23.195 
_':;.166 
23.136 
23.106 

2      9 
2      9  2 
2       9  I 
2      9.6 
2      9.8 

2751 

27.863 

27.820 

27.777 
27.734 

2 
2 
■  > 
2 
2 

18 

185 

ls.4 
18.6 
18.8 

26.086 
26.048 
26.011 
25573 
25536 

2 
2 
o 

2 
2 

27 
27  2 
27.4 

27\8 

24.4,89 
24.456 
24.423 

24..".:"i 
24.337 

2 
2 
•  > 
2 
2 

36 

36.2 

36.4 

■oCkC 

23.076 
2: 1.334 
23.017 
22.988 

22.959 

2     10 

2     10.2 
2     10.4 
2     10.6 
2     10.8 

27.1 

27.649 

27.607 

27.665 

27.522 

o 

2 

9 
2 

O 

19 
19.2 
19.4 
19.6 

19.8 

-99 
25562 
25524 

25. 7  -7 
25.750 

2 
2 
2 
2 

•  > 

28.2 

2S.4 
28.6 

24.324 
24.291 
24.258 
24  226. 
24.193 

2 
2 
o 

•  > 

37 
37.2 

;;7.4 
37.6 

22.930 
22500 
22.871 
22542 
22513 

490 


The   Naval   Constructor 


SPEED  TABLES.  —  (Continued.) 


1  Knot 

Admi- 

1  Knot 

Admi- 

1 

Knot 

Admi- 

1 Knot 

Admi- 

in  = 
Min.  Sec 

.  RALTY 
'  KNOTS 
'  Per  Hr. 

in   = 
Miii.  Sec 

.  KALTY 

"  Knots 
•  Per  Hr. 

IN'      = 

Min.  Sec 

ralty 
"  Knots 
■  Per  Hr. 

in   = 
Min.  Sec 

ralty 
"  Knots 
•  Per  Hr. 

2 

38 

22.784 

o 

47 

21.556 

2 

56 

20.454 

3 

25 

17.560 

2 

38.2 

22.756 

2 

47.2 

21531 

2 

56.2 

20.431 

•J 
O 

26 

17.475 

2 

38.4 

22.727 

2 

47.4 

21.505 

2 

56.4 

20.408 

3 

27 

17.391 

2 

38.6 

22.698 

2 

47.6 

21.479 

2 

56.6 

20.385 

3 

28 

17.307 

2 

38.8 

22.670 

2 

47.8 

21.454 

2 

56.8 

20.361 

3 

29 

17.225 

2 

39 

22.646 

2 

48 

21.428 

2 

57 

20.338 

3 

30 

17.142 

2 

39.2 

22.613 

2 

48.2 

21.403 

2 

57.2 

20.316 

3 

31 

17.061 

2 

39.4 

22.584 

2 

48.4 

21.377 

2 

57.4 

20.293 

3 

32 

16.981 

2 

39.6 

22.556 

2 

48.6 

21  352 

2 

57.6 

20.270 

3 

33 

16.901 

2 

39.8 

22.528 

2 

48.8 

21.327 

2 

57.8 

20.247 

3 

34 

16.822 

2 

40 

22.500 

2 

49 

21.302 

2 

58 

20.224 

3 

35 

16.744 

2 

40.2 

22.471 

2 

49.2 

21.276 

2 

58.2 

20.202 

3 

36 

16.667 

2 

40.4 

22.443 

2 

49.4 

21.251 

2 

58.4 

20.179 

3 

37 

16.590 

2 

40.6 

22.415 

2 

49.6 

21.226 

2 

58.6 

20.156 

3 

38 

16.514 

2 

40.8 

22.388 

2 

49.8 

21.201 

Q 

58.8 

20.134 

3 

39 

16.438 

2 

41 

22.360 

2 

50 

21.176 

2 

59 

20.111 

3 

40 

16.363 

2 

41.2 

22.332 

2 

50.2 

21.151 

2 

59.2 

20.089 

3 

41 

16.289 

2 

41.4 

22.304 

9 

£1 

50.4 

21.126 

2 

59.4 

20.0G6 

o 
O 

42 

16.216 

2 

41.6 

22.277 

2 

50.6 

21.101 

2 

59.6 

20.044 

3 

43 

16.143 

2 

41.8 

22.249 

2 

50.8 

21.077 

2 

59.8 

20.022 

3 

44 

16.071 

2 

42 

22.222 

2 

51 

21.052 

3 

0 

20.000 

3 

45 

16.000 

2 

42.2 

22.194 

2 

51.2 

21.028 

3 

1 

19.890 

3 

46 

15.929 

2 

42^4 

22.167 

2 

51.4 

21.003 

3 

2 

19.780 

3 

47 

15.859 

2 

42.6 

22.140 

9 

it 

51.6 

20.978 

3 

*> 

o 

19.672 

3 

48 

15.789 

2 

42.8 

22.113 

9 

51.8 

20.954 

Q 

4 

19.564 

3 

49 

15.721 

2 

43 

22.086 

2 

52 

20.930 

3 

5 

19.460 

3 

50 

15.652 

2 

43.2 

22.058 

2 

52.2 

20.905 

3 

6 

19.355 

3 

51 

15.584 

2 

43.4 

22.031 

2 

52.4 

20.881 

o 
O 

7 

19.251 

3 

52 

15.517 

2 

43.6 

22.004 

2 

52.6 

20.857 

3 

8 

19.150 

3 

53 

15.450 

2 

43.8 

21.978 

2 

52.8 

20.833 

3 

9 

19.047 

3 

54 

15.384 

2 

44 

21.951 

2 

53 

20.808 

3 

10 

18.947 

3 

55 

15.319 

2 

44.2 

21.924 

2 

53.2 

20.784 

3 

11 

18.848 

3 

56 

15.254 

2 

44.4 

21.897 

2 

53.4 

20.761 

3 

12 

18.750 

3 

57 

15.190 

2 

44.6 

21.871 

2 

53.6 

20.737 

3 

13 

18.652 

*> 
O 

58 

15.126 

2 

44.8 

21.844 

2 

53.8 

20.713 

3 

14 

18.556 

3 

59 

15.062 

2 

45 

21.818 

2 

54 

20.689 

3 

15 

18.461 

4 

00 

15.000 

2 

45.2 

21.791 

2 

54.2 

20.665 

3 

16 

18.367 

4 

1 

14.938 

2 

45.4 

21.765 

2 

54.4 

20.642 

3 

17 

18.274 

4 

2 

14.876 

2 

45.6 

21.739 

2 

54.6 

20.618 

3 

18 

18.181 

4 

3 

14.815 

2 

45.8 

21.712 

2 

54.8 

20.594 

3 

19 

18.090 

4 

4 

14.754 

2 

46 

21.6S6 

2 

55 

20.571 

3 

20 

18.000 

4 

5 

14.694 

2 

46.2 

21.660 

2 

55.2 

20.547 

3 

21 

17.910 

4 

6 

14.634 

2 

46.4 

21.634 

2 

55.4 

20.524 

3 

22 

17.823 

4 

7 

14.575 

2 

46.6 

21.608 

2 

55.6 

20.501 

3 

23 

17.734 

4 

8 

14.516 

2 

46.8 

21.582 

2 

55.8 

20.477 

3 

24 

17.647 

4 

9 

14.457 

Speed  Tables 


491 


SPEED    TABLES.  —  (Continued.) 


1  Knot 

Aioii- 

1 

Kxi  it 

Admi- 

i Knot 

A  I>MI- 

1  Knot 

A  I>MI- 

IN     = 

Min.  Sec 

B  \LTY 
K> 

■  Per  Hr. 

IN      = 

Miu.  Sec 

ralty 

"  Knots 
•Per  Hi. 

IN     = 
Min.  See 

B  A  I    IV 

'  Km  i  M 
'Per  Br. 

in    = 
Min.  Sec 

.   R  W/I  Y 

■  Kn'i  ra 
Per  Hr. 

4     10 

14.400 

4 

55 

12.203 

5 

40 

10.588 

6 

25 

9. .350 

4     11 

14.342 

4 

56 

12.162 

5 

41 

10.557 

6 

26 

9.326 

4     12 

14.  ■_'-.-, 

4 

57 

12.121 

5 

42 

10.526 

6 

27 

9.302 

4     13 

14.220 

4 

58 

12.080 

5 

43 

10.495 

6 

28 

9.278 

4     14 

14.173 

4 

59 

12.040 

5 

44 

10.4(55 

6 

29 

9.254 

4    15 

14.118 

5 

00 

12.000 

5 

45 

10.434 

6 

30 

9.230 

4     16 

14.063 

5 

1 

11.960 

5 

46 

10.404 

6 

31 

9.2<  >7 

4     17 

14.008 

5 

•» 

11.920 

5 

47 

10.375 

6 

32 

9.183 

4     18 

13.953 

5 

3 

11.880 

5 

48 

10.345 

6 

33 

9.160 

4     19 

13.900 

5 

4 

11.841 

5 

49 

10.315 

6 

34 

9.137 

4    20 

13.846 

5 

5 

11.803 

5 

50 

10.2S6 

6 

35 

9.113 

4    21 

13.793 

5 

6 

11.764 

5 

51 

10.256 

6 

36 

9.090 

4    22 

13.740 

5 

7 

11.726 

5 

52 

10.227 

6 

37 

9.068 

4    23 

13.688 

5 

8 

11.688 

5 

53 

10.198 

6 

38 

9.044 

4    24 

13.636 

5 

9 

11.650 

5 

54 

10.169 

6 

39 

9.022 

4    25 

13.5S4 

5 

10 

11.613 

5 

55 

10.140 

6 

40 

9.000 

4    26 

13.5&3 

5 

11 

1 1 .575 

5 

56 

10.112 

6 

41 

8.977 

4     27 

13.483 

5 

12 

11.538 

5 

57 

10.084 

6 

42 

8.955 

4    28 

13.432 

5 

13 

11.501 

5 

58 

10.055 

6 

43 

8.933 

4    29 

13.383 

5 

14 

11.465 

5 

59 

10.027 

6 

44 

8.911 

4    30 

13.333 

5 

15 

11.428 

6 

00 

10.000 

6 

45 

8.889 

4    31 

13.284 

•"> 

16 

11.392 

6 

1 

9.972 

6 

46 

8.867 

4    32 

13.235 

5 

17 

11.356 

6 

2 

9.944 

6 

47 

8.845 

4    33 

13.186 

5 

18 

11.323 

6 

3 

9.917 

6 

48 

8.823 

4    34 

13.138 

5 

19 

11.285 

6 

4 

9.890 

6 

49 

8.801 

4    35 

13.092 

5 

20 

11.250 

6 

5 

9.863 

6 

50 

8.780 

4    36 

13.043 

•"> 

21 

11.214 

6 

6 

9.830 

6 

51 

8.759 

4    37 

12.996 

5 

22 

11.180 

6 

7 

9.809 

6 

52 

8.737 

4    38 

12.950 

5 

2:i 

11.146 

6 

8 

9.783 

6 

53 

8.716 

4    39 

12.903 

5 

24 

11.111 

6 

9 

9.756 

6 

54 

8.695 

4    40 

12.857 

5 

25 

11.077 

6 

10 

9.729 

6 

55 

8.675 

4    41 

12.811 

5 

26 

11.043 

6 

11 

9.703 

6 

56 

8.654 

4    42 

12.766 

5 

27 

11.009 

6 

12 

9.677 

6 

57 

8.633 

4    43 

12.720 

5 

28 

10.97." 

6 

13 

9.651 

6 

58 

8.612 

4    44 

1 2.676 

5 

29 

10.94-J 

6 

14 

9.625 

6 

59 

•  --,91 

4    45 

12.631 

r» 

30 

10.909 

6 

15 

9.600 

7 

00 

8.571 

4    40 

12.687 

5 

31 

10.876 

6 

16 

9.574 

•7 

1 

8.551 

4    47 

12.543 

5 

32 

10.843 

6 

17 

9.54: » 

*1 

2 

8.530 

4     4^ 

12.500 

5 

33 

10.810 

6 

18 

9.524 

"7 

3 

8.510 

4     49 

1J456 

5 

34 

10.77 

6 

19 

9.490 

4 

8.490 

4    50 

12.413 

5 

35 

10.746 

6 

20 

9.473 

7 

5 

8.470 

4    51 

12..v.71 

5 

36 

10.714 

6 

21 

9.448 

r* 

6 

8.450 

4    52 

12.329 

5 

37 

10.' 

6 

22 

9. 424 

*■* 

7 

8.430 

4 

12.287 

5 

38 

10.651 

6 

23 

9.399 

~ 

8 

8.41.; 

4    74 

12.245 

5 

39 

10.61  i» 

6 

21 

9.375 

9 

8.39J 

492 


The   Naval   Constructor 


SPEED  TABLES.  —  (Concluded.) 


1  Knot 
in    = 
Min.  Sec. 

Admi- 
ralty 

Knots 
Per  Hr. 

1  Knot 

in    = 
Min.  See. 

'Admi- 
ralty 
Knots 
Per  Hr. 

1  Knot 

in    = 
Min.  Sec 

Admi- 

.  RALTY 

■  Knots 
Per  Hr. 

1  Knot 
in    = 

Min.  Sec 

Admi- 
ralty 
Knots 
Per  Hr. 

7    10 

8.372 

7 

35 

7.912 

7 

55 

7.579 

8 

15 

7.272 

7     11 

8.353 

7 

36 

7.895 

7 

56 

7.563 

8 

16 

7.258 

7    12 

8.334 

1 

37 

7.877 

7 

57 

7.547 

8 

17 

7.243 

7    13 

8.315 

7 

38 

7.860 

7 

58 

7.531 

8 

18 

7.229 

7    14 

8.295 

7 

39 

7.843 

7 

59 

7.515 

8 

19 

7.214 

7    15 

8.276 

7 

40 

7.826 

8 

0 

7.500 

8 

20 

7.200 

7     16 

8.257 

7 

41 

7.809 

8 

1 

7.484 

8 

21 

7.185 

7     17 

8.228 

7 

42 

7.792 

8 

o 

7.468 

8 

22 

7.171 

7     18 

8.219 

7 

43 

7.775 

8 

3 

7.453 

8 

23 

7.157 

7    19 

8.200 

7 

44 

7.758 

8 

4 

7.438 

8 

24 

7.142 

7    20 

8.181 

7 

45 

7.741 

8 

5 

7.422 

8 

25 

7.128 

7    21 

8.163 

7 

46 

7.725 

8 

6 

7.407 

8 

26 

7.114 

7    22 

8.144 

7 

47 

7.708 

8 

7 

7.392 

8 

27 

7.100 

7    23 

8.127 

7 

48 

7.692 

8 

8 

7.377 

8 

28 

7.086 

7    24 

8.108 

1 

49 

7.675 

8 

9 

7.362 

8 

29 

7.072 

7    25 

8.090 

( 

50 

7.659 

8 

10 

7.346 

S 

30 

7.059 

7    26 

8.071 

7 

51 

7.643 

8 

11 

7.331 

8 

31 

7.045 

7    27 

8.053 

7 

52 

7.627 

8 

12 

7.317 

8 

32 

7.031 

7    28 

8.035 

7 

53 

7.611 

8 

13 

7.302 

8 

33 

7.017 

7    29 

8.017 

7 

54 

7.595 

8 

14 

7.287 

8 

34 

7.004 

7    30 

8.000 

.... 

.... 

.... 

7    31 

7.982 

.... 

.... 

.... 

7    32 

7.964 

.  .  .  • 

.... 

.... 

7    33 

7.947 

.... 

.... 

.... 

7    34 

7.929 

.... 

■  •  •  • 

.... 

Section  VII. 

MATHEMATICAL   TABLES. 


493 


The  Metric  System. 


4'.':. 


THE    METRIC   SYSTEM. 

The  principal  advantage  of  the  metric  system  consists  in  its  use  of  the 


1 


of 


decimal  subdivisions.    The  attempt  to  consider  the  metre  as 

a  quadrant  of  the  earth's  surface-  has  been  abandoned,  and  it  is  dow  held 
only  to  be  the  length  of  the  standard  known  as  the  Metre  de»  Arch 
copies  of  which  arc  issued  by  the  Bureau  Jut'  rnationale  <i>  8  Pcddset  MCxures, 
at  Breteuil,  near  Paris.  ,   ,       ,  .  ..    .         .. 

The  kill  gramme  was  originally  intended  to  be  the  weigntof  a  cubic 
decimetre  or  litre  of  pure  water  at  the  temperature  of  maximum  density, 
but  it  is  really  now  considered  only  as  the  weight  of  a  platinum  standard. 
At  the  same  time,  this  relation  between  the  unit  of  weight  and  a  Standard 
volume  of  water  is  sufficiently  close  for  the  specific  gravity  of  any  sub- 
stance to  be  considered  as  equal  to  the  weight  of  a  cubic  decimetre  of  that 
Bubstance  In  all  hydraulic  measurements  a  cubic  metre  of  water  is  equal 
in  weight  to  the  metric  tonne  of  1000  kilogrammes,  a  most  convenient  fact 
in  the  determination  if  the  power  developed  by  a  given  fall  and  volume 
of  water. 

The  French  Metrical  System. 


The  French  units  of  weight,  measure,  and 
feet  decimal  system, except  those  of  time  and 
multiplication  of  the  units  are  expressed  by 
follows  : 

Lndn,  Division. 
Milli  =  1000th  of  the  unit.  Deca 

Centi  =  100th  of  the  unit.  Hecato 

Deci         10th  Of  the  unit.  Kilio 

Metre,     litre,     stere,     are,     franc,    Myrio 
gramme. 

French  Measure  of  Length 

1  millimetre     =    0.03987  inch. 
1  centimetre     =   0.3937  inch. 
1  decimetre      =    3.937  inches. 
1  metre  (unit)  =--  39.37  inches. 
1  sea  mile         =  1853.25  metres. 
1  kilometre      =  0.53959  sea  mile. 


coin  are  arranged  into  a  per- 

the  circle.    The  division  and 

Latin  and  Greek  names,  as 

Greek,  Multiplication. 

=  10  times  the  unit. 
=  100  times  the  unit. 
=  1000  times  the  unit. 
=  10000  times  the  unit. 


1  metre  (unit) 
1  decametre 
1  hectometre 
1  kilometre 


1  statute  mile 
1  kilometre 


=       3.28083  feet. 
=     32.8083  feet. 
=   328.083  feet. 

=  3280.83  ft.  =  0.62137 
mile. 

=  .      1.60935  kilomets. 
=      49.7096  chains. 


1  square  metre 
1  are 
1  decare 
1  hectare 


1  stere  (cubic) 
metre)         j* 
i  Btere 
1  litre 
1  decistere 


1  ton 

1  ton 

1  kilogramme 
1  hectogramme 
l  decagrami 

1  gramme 

1  French  ton 


French  Measure  of  Surface. 

1  are  =  1076.4  square  feet. 

1  decare  =    107. 64  square  feet. 

1  hectare  =       2.471  Eng.  acres. 

1  square  mile  =  259  hectares. 


10.764  square  feet. 
100  square  metres 
10  ares. 
100  a 


French  Measure  of  Volume. 


10  decasteres. 

1000  litres. 

1  cubic  decimetre. 

3.5314  cubic  fe< 


1  stere         =  35.31 1  Fug.  cubic  feet. 
1  lit  =  61.023  Eng.  cub. inches. 

1  gallon  7854  litres, 

1  decistere  =    2.838  bushels  (nearly). 


French  Measure  of  Weight. 


1  cubic  metre  dis- 
tilled water. 

1000  kilogrammes. 

1000  grammes. 

loo  gramm<  - 

10  grami 

1  cubic  centin 
distilled  water. 

0.9842  Eng.  ton. 


1  gramme 
l  decigramme  < 
i  centigramme 
1  kilogramme   ■ 

1  Eng.  pound 
1  gramme 
l  English  ton 


10  decigrammes. 

10  centigrammes. 

10  milligranraM  - 

2.20462  pounds  av- 
oirdupois 
0. 15359  kilograms. 

15.  13  grains  troy. 
1.016  French  tons. 


490 


The  Metric  System. 


Conversion 

of  English 

Inches  into 

Centimetres. 

Inches. 

0 

1 

2 

3 

Cm. 

4 

5 

6 

7 

8 

9 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

0 

0.000 

2.540 

5.080 

7.620 

10.16 

12.70 

15.24 

17.78 

20.32 

22.86 

10 

25.40 

27.94 

30.48 

33.02 

35.56 

38.10 

40.64 

43.18 

45.72 

48.26 

20 

50.80 

53. 34 

55.88 

58.42 

60.96 

63.50 

66.04 

68.58 

71.12 

73.66 

30 

76.20 

78.74 

81.28 

83.82 

86.36 

88.90 

91.44 

93.98 

96.52 

99.06 

40 

101.60 

104.14 

106.68 

109.22 

111.76 

114.30 

116.84 

119.38 

121.92 

124.46 

50 

127.00 

129.54 

132.08 

134.62 

137.16 

139.70 

142.24 

144.78 

147.32 

149.86 

60 

152.40 

154.94 

157.4S 

160.02 

162.56 

165.10 

167.64 

170.18 

172.72 

175.26 

70 

177.80 

180.34 

182.88 

185.42 

187.96 

190.50 

193.04 

195.58 

198.12 

200.96 

80 

203.20 

205.74 

208.28 

210.82 

213.36 

215.90 

218.44 

220.98 

223.52 

226.06 

90 

228.60 

231.14 

233.68 

236.22 

238.76 

241.30 

243.84 

246.38 

248.92 

251.46 

100 

254.00 

256.54 

259.08 

261.62 

264.16 

266.70 

269.24 

271.78 

274.32 

276.85 

Conversion 

of  Centimetres  into  English  Inches. 

Cm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

0 

0.000 

0.394 

0.787 

1.181 

1.575 

1.969 

2.362 

2.756 

3.150 

3.543 

10 

3.937 

4.331 

4.742 

5.118 

5.512 

5.906 

6.299 

6.693 

7.087 

7.480 

20 

7.874 

8.268 

8.662 

9.055 

9.449 

9.843 

10.236 

10.630 

11.021 

11.418 

30 

11.811 

12.205 

12.599 

12.992 

13.386 

13.780 

14.173 

14.567 

14.961 

15.355 

40 

15.748 

16.142 

16.536 

16.929 

17.323 

17.717 

18.111 

18.504 

18.898 

19.292 

50 

19.685 

20.079 

20.473 

20.867 

21.260 

21.654 

22.048 

22.441 

22.835 

23.229 

60 

23.622 

24.016 

24.410 

24.804 

25.197 

25.591 

25.985 

26.378 

26.772 

27.166 

70 

27.560 

27.953 

28.347 

28.741 

29.134 

29.528 

29.922 

30.316 

30.709 

31.103 

80 

31.497 

31.890 

32.284 

32.678 

33.071 

33.465 

33.859 

34.253 

34.646 

35.040 

90 

35.434 

35.827 

36.221 

36.615 

37.009 

37.402 

37.796 

38.190 

38.583 

38.977 

100 

39.370 

39.764 

40.158 

40.552 

40.945 

41.339 

41.733 

42.126 

42.520 

42.914 

Conversion  of  Engl 

ish  Feet  into  Metres. 

Feet. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

0 

0.000 

0.3048 

0.6096 

0.9144 

1.2192 

1.5239 

1.8287 

2.1335 

2.4383 

2.7431 

10 

3.0479 

3.3527 

3.6575 

3.9623 

4.2671 

4.5719 

4.8767 

5.1815 

5.4863 

5.7911 

20 

6.0359 

6.4006 

6.7055 

7.0102 

7.3150 

7.6198 

7.9246 

8.2294 

8.5342 

8.8390 

30 

9.1438 

9.4486 

9.7534 

10.058 

10.363 

10.668 

10.972 

11.277 

11.582 

11.887 

40 

12.192 

12.496 

12.801 

13.106 

13.411 

13.716 

14.020 

14.325 

14.630 

14.935 

50 

15.239 

15.544 

15.849 

16.154 

16.459 

16.763 

17.068 

17.373 

17.678 

17.983 

60 

18.287 

18.592 

18.897 

19.202 

19.507 

19.811 

20.116 

20.421 

20.726 

21.031 

70 

21.335 

21.640 

21.945 

22.250 

22.555 

22.859 

23.164 

23.469 

23.774 

24.079 

80 

24.383 

24.688 

24.993 

25.298 

25.602 

25.907 

26.212 

26.517 

26.822 

27.126 

90 

27.431 

27.736 

28.041 

28.346 

28.651 

28.955 

29.260 

29.565 

29.870 

30.174 

100 

30.479 

30.784 

31.089 

31.391 

31.698 

32.003 

32.308 

32.613 

32.918 

33.222 

Convers 

ion  of  Metres  into  English  Feet. 

Metres. 

0 

1 

2 

3 

4 

5 

6 

.7 

8 

9 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

0 

0.000 

3.2809 

6.5618 

9.8427 

13.123 

16.404 

19.685 

22.966 

26.247 

29.528 

10 

32.809 

36.090 

39.371 

42.651 

45.932 

49.213 

52.494 

55.775 

59.056 

62.337 

20 

65.618 

68.899 

72.179 

75.461 

78.741 

82.022 

85.303 

88.584 

91.865 

95.146 

30 

98.427 

101.71 

104.99 

108.27 

111.55 

114.83 

118.11 

121.39 

124.67 

127.96 

40 

131.24 

134.52 

137.80 

141.08 

144.36 

147.64 

150.92 

154.20 

157.48 

160.76 

50 

164.04 

167.33 

170.61 

173.89 

177.17 

180.45 

183.73 

187.01 

190.29 

193.57 

60 

196.85 

200.13 

203.42 

206.70 

209.98 

213.26 

216.54 

219.82 

223.10 

226.38 

70 

229.66 

232.94 

236.22 

239.51 

242.79 

246.07 

249.35 

252.63 

255.91 

259.19 

80 

262.47 

265.75 

269.03 

272.31 

275.60 

278.88 

282.16 

285.44 

288.72 

292.00 

90 

295.28 

298.56 

301.84 

305.12 

308.40 

311.69 

314.97 

318.25 

321.53 

324.81 

100 

328.09 

331.37 

334.65 

337.93 

341.21 

344.49 

347.78 

351.06 

354.34 

357.32 

The  Metric  System. 


497 


Conversion  of  English  Statute 

-miles  Into 

Kilometres. 

Mil««. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

0 

0.0000 

1.6093 

3.2186 

4.8279 

6.4372 

• 

- 

11.2652  12,8745 

14.4848 

10 

16.093 

17.702 

19.312 

20.921 

. 

24.139 

25.749 

27. 

- 

30.577 

20 

32.186 

33.795 

35.405 

37.014 

38.623 

40.232 

41.842 

43.451 

45.060 

46.670 

18.279 

51.498 

53.107 

r>).7  it; 

56.325 

57.935 

61.153 

62.763 

40 

- 

67.591 

69.200 

70.809 

72.418 

74.028 

77.246 

50 

- 

• 

- 

86.902 

88.51 1 

90.121 

91.730 

94.949 

60 

98.167 

99.777 

101.39 

102.99 

104.60 

106.21 

107.82 

109.43 

111.04 

70 

112.65 

114.26 

115.87 

117.4- 

119.08 

120.69 

122.30 

125.52 

127.13 

80 

128.74 

' 

131.96 

133.57 

135.17 

1  16.78 

-     1 

1 10.00 

141.61 

143.22 

90 

144.85 

146.44 

148.05 

1 19.66 

151.26 

» 

156.09 

157.70 

159.31 

100 

• 

- 

164.14 

'    • 

172.18 

173.79 

175.40 

Conversion  of 

Kilom 

etres 

into  Englis 

h  Statute=miles. 

Kiloui. 

• 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Milts. 

Miles. 

0 

0.0000 

0.6214 

1.2427 

1.8641 

2.4855 

3.1069 

3  7282 

4.3497 

4.9711 

5.5924 

10 

6.2138 

-     - 

7. 1565 

8.0780 

8.6994 

9.3208 

9.9421 

10.562 

11.185 

1 1  .<.!  "5 

20 

12. 127 

13.049 

14.292 

14.913 

15.534 

16.156 

17.399 

18.019 

30 

18.641 

19.263 

-■ 

_ 

21.127 

21.748 

22.370 

22.990 

23.613 

- 

40 

24.855 

25. 177 

- 

26.720 

27 

28.584 

29.204 

29.827 

30.447 

50 

31.069 

31.690 

32.311 

32.933 

33.554 

34.17:. 

34.797 

35.417 

36.040 

36.660 

60 

?     - 

37.904 

• 

39.147 

39.768 

• 

41.011 

41.631 

42.254 

12.874 

70 

43.497 

44.118 

44.739 

45.361 

45.982 

46.603 

17.22 

47.845 

48.468 

49.088 

80 

49.711 

50.332 

50.953 

51.575 

52.196 

52.817 

53.439 

54.059 

54.682 

55.302 

90 

55.924 

57.166 

57.788 

58.409 

59.030 

60.272 

60.895 

61.515 

100 

62.138 

G2.759 

63.380 

64.002 

64.623 

65.244 

65.866 

67.109 

67.729 

Conversion  of  Sea=miles  into  Kilometres. 

Sea-miles. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

0 

0.0000  1.8532 

3.7046 

5.5596 

7.4128 

9.2660 

11.119 

12.972 

•    788 

10 

18.532  20.386 

\i::s\: 

24.128 

25. 94:. 

27.798 

29.6^1 

31.504 

33.357 

35.320 

20 

37.01 

38.918 

40.769 

44.477 

46.331 

48.183 

50.0:36 

51.889 

53.852 

30 

55.5% 

57.450 

59.301 

61.192 

63.009 

64.863 

66.715 

68.568 

70.421 

72.384 

40 

74. 12> 

75.982 

77.833 

81.541 

83.396 

85.247 

87.100 

88.953 

90.916 

50 

92.660 

94.514 

96.365 

98.256 

100.07 

101.92 

103.78 

105.63 

107.48 

109.45 

60 

111.19 

113.05 

114.90 

116.79 

118.61 

120.45 

122.21 

124.16 

126.01 

127.98 

70 

129.72 

131.58 

133.43 

135.32 

137.14 

139.98 

140.74 

142.69 

144.54 

1 16.51 

80 

148.25  L50.il 

151.96 

155.67 

159.27 

161.22 

163.07 

165.04 

90 

166.78;  168.64 

170.49 

172.38 

174.20 

176.05 

177.80 

179.75 

181.60 

" 

100 

185.32  187.18 

189.03 

190.88 

192.73 

191.:.- 

196.44 

198.28 

200.14 

201.99 

Conversion  of 

Kilometres 

into 

Sea=miles. 

Kilom. 

0 

1 

2 

3 

4 
Sea-m. 

5 

6 

7 

8 

9 

Bea-m. 

- 

Sea-in. 

Sea-m. 

Sea-m. 

• 

Sea-m 

Sea-m 

Sea-m, 

0 

0.0000 

0.53% 

1.079-2 

1.6188 

2.1584 

3. 2: -.75 

-.7771 

4.3167 

1  • 

10 

" 

6.4751 

7.0147 

7.5543 

-    - 

- 

9.1730 

9.7126 

10.252 

20 

10.792 

11.331 

11.870 

12.410 

12.950 

14.029 

14.568 

15.108 

15.647 

30 

16.188 

16.727 

17.265 

17.8% 

18     ■ 

:-  37 

19.424 

' 

20.504 

21.044 

40 

21.584 

22.123 

22.661 

_ 

2:;. 7  in 

'J  1.271 

24.819 

25.360 

25.900 

- 

50 

26.980 

27.519 

28 

28.598 

29.135 

30.214 

30.757 

31.296 

• 

60 

.    -" 

32.915 

33.994 

34.530 

35.063 

36.692 

37.231 

70 

37.771 

38.310 

:;—■"■- 

40.459 

41.004 

41.574 

12.088 

42.627 

80 

43.167 

1    " 

14.284 

44.786 

45.320 

■ 

46.399 

46.943 

47.1-:: 

48.023 

90 

53  49.103 

49.644 

50.182 

60.715 

51.251 

51.794 

53.419 

100 

53.959  54.498 

55.038 

55.575 

56.117 

56.668 

57.198 

57.737 

58.276 

58.816 

498 


The  Metric  System. 


Con 

version  of  Square  Inches  into  Square  Centimetres. 

Square  in. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Cm-'. 

Cm3. 

Cm'-. 

Cm*. 

Cm2. 

Cm2. 

Cm2. 

Cm2. 

Cm2. 

Cm2. 

0 

0.0000 

6.4515 

12.903 

19.35-4 

25.806 

32.257 

38.709 

45.160 

51.612 

58.063 

10 

64.515 

70.967 

77.418 

83.869 

90.321 

96.772 

103.22 

109.67 

116.12 

122.57 

20 

129.03 

135.48 

141.93 

148.38 

154.83 

161.29 

167.74 

174.19 

180.64 

187.09 

30 

193.54 

199.99 

206.44 

212.89 

219.34 

225.  SO 

231.25 

238.70 

245.15 

251.60 

40 

258.06 

264.51 

270.96 

277.41 

283.86 

290.32 

296.77 

303.22 

309.67 

316.12 

50 

322.57 

329.02 

335.47 

341.92 

348.37 

351.83 

361.28 

367.73 

374.18 

380.63 

60 

387.09 

393.54 

399.99 

406.44 

412.89 

419.35 

425.80 

432.25 

438.70 

445.15 

70 

451.60 

458.05 

464.50 

470.95 

477.40 

483.86 

490.31 

496.76 

503.21 

509.66 

80 

516.12 

522.57 

529.02 

535.47 

541.92 

548.38 

554.83 

561.28 

567.73 

574.18 

90 

580.63 

587.08 

593.53 

599.98 

606.43 

612.89 

619.34 

625.79 

632.24 

638.69 

100 

645.15 

651.60 

658.05 

664.50 

670.95 

677.41 

683.86 

690.31 

696.76 

703.21 

Conversion  of  Square  Centimetres  into  Square  Inches. 

Square  cm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

In2. 

In2. 

In2. 

In2. 

In2. 

In2. 

In2. 

In2. 

In9-. 

In2. 

0 

0.0000 

0.1550 

0.3100 

0.4650 

0.6200 

0.7750 

0.9300 

1.0850 

1.2400 

1.3950 

10 

1.5500 

1.7050 

1.8600 

2.0150 

2.1700 

2.3250 

2.4800 

2.6350 

2.7900 

2.9450 

20 

3.1000 

3.2550 

3.4100 

3.5650 

3.7200 

3.8750 

4.0300 

4.1850 

4.3400 

4.4950 

30 

4.6501 

4.8051 

4.9601 

5.1151 

5.2701 

5.4251 

5.5801 

5.7351 

5.8901 

6.0451 

40 

6.2001 

6.3551 

6.5101 

6.6651 

6.8201 

6.9751 

7.1301 

7.2851 

7.4401 

7.5951 

50 

7.7501 

7.9051 

8.0601 

8.2151 

8.3701 

8.5251 

8.6801 

8.8351 

8.9901 

9.1451 

60 

9.3002 

9.4552 

9.6102 

9.7652 

9.9202 

10.075 

10.230 

10.385 

10.540 

10.695 

70 

10.850 

11.040 

11.160 

11.315 

11.470 

11.625 

11.780 

11.935 

12.090 

12.245 

80 

12.400 

12.555 

12.710 

12.865 

13.020 

13.175 

13.330 

13.485 

13.640 

13.795 

90 

13.950 

14.105 

14.260 

14.415 

14.570 

14.725 

14.880 

15.035 

15.190 

15.345 

100 

15.500 

15.655 

15.810 

15.965 

16.120 

16.275 

16.430 

16.585 

16.740 

16.895 

Conversion  of  Cubi 

c  Inch 

es  Into  Cub 

ic  Centimetres. 

Cubic  in. 

b 

1 

2 

3 

4 

5 

6 

7 

8 

Cm3. 

9 

Cm3. 

Gm». 

Cm3. 

Cm3. 

Cms, 

Cm3. 

Cm3. 

Cm3. 

Cm3. 

0 

0.0000 

16.383 

32.773 

49.160 

65.546 

81.933 

98.320 

114.71 

131.01 

147.48 

10 

163.87 

180.26 

196.64 

213.03 

229.41 

245.80 

262.19 

278.58 

294.88 

311.35 

20 

327.73 

344.12 

360.50 

376.89 

393.27 

409.66 

426.05 

442.44 

458.74 

475.21 

30 

491.60 

507.99 

524.37 

540.76 

557.14 

573.53 

569.92 

606.31 

622.61 

639.08 

40 

655.46 

671.85 

688.23 

704.52 

721.00 

737.39 

753.78 

770.17 

786.47 

802.94 

50 

819.33 

835.72 

851.10 

868.49 

884.87 

901.26 

917.65 

934.04 

950.34 

966.81 

60 

983.20 

999.59 

1016.0 

1032.4 

1048.7 

1065.1 

1081.5 

1097.9 

1114.2 

1130.7 

70 

1147.1 

1163.5 

1179.9 

1196.3 

1212.6 

1229.0 

1245.4 

1261.8 

1278.1 

1294.6 

80 

1310.9 

1327.3 

1343.7 

1360.1 

1376.4 

1392.8 

1409.2 

1425.6 

1441.9 

1458.4 

90 

1474.8 

1491.2 

1507.6 

1524.0 

1540.3 

1556.7 

1573.1 

1589.5 

1605.8 

1622.3 

100 

1638.7 

1655.1 

1671.5 

1687.9 

1704.2 

1720.6 

1737.0 

1753.4 

1769.7 

1786.2 

Conversion  of  Cubic  Centimetres  into  Cub 

ic  Inches. 

Cubic  cm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

In3. 

In3. 

In3. 

In3. 

In3. 

'in3. 

In3. 

In3. 

In3. 

In3. 

0 

0.0000 

0.0610 

0.1221 

0.1831 

0.2441 

0.3051 

0.3661 

0.4272 

0.4882 

0.5492 

10 

0.6102 

0.6712 

07323 

0.7933 

0.8543 

0.9153 

0.9763 

1.0374 

1.0984 

1.1594 

20 

1.2205 

1.2815 

1.3426 

1.4036 

1.4646 

1.5256 

1.5866 

1.6477 

1.7087 

1.7697 

30 

1.8308 

1.8918 

1.9529 

2.0139 

2.0749 

2.1359 

2.1969 

2.2580 

2.3190 

2.3800 

40 

2.4410 

2.5020 

2.5631 

2.6241 

2.6851 

2.7461 

2.8071 

2.8682 

2.9292 

2.9902 

50 

3.0513 

3.1123 

3.1734 

3.2344 

3.2954 

3.3564 

3.4174 

3.4785 

3.5395 

3.6005 

60 

3.6615 

3.7225 

3.7836 

8.8446 

3.9056 

3.9666 

4.0276 

4.0887 

4.1497 

4.2107 

70 

4.2718 

4.3328 

4.3939 

4.4549 

4.5159 

4.5769  4.6379 

4.6990 

4.7600 

4.8210 

80 

1.8820 

4.9430 

5.0041 

5.0651 

5.1261 

5.1871 

5.2481 

5.3092 

5.3702 

5.4312 

90 

5.4923 

5.5533 

5.6144 

5.6754 

5.7364 

5.7974 

5.8584 

5.9195 

5.9805 

6.0415 

100 

6.1025 

6.1635 

6.2246 

6.2856 

6.3466 

6.4076 

6.4686 

6.5297 

6.5907 

6.6517 

The  Metric  System. 


499 


Conversion  of  Ci 

Libic  Yards 

nto   C 

ubic  Metres 

. 

Cubic  yds. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Met^. 

Met*. 

Met^. 

Met'. 

Met  . 

Met^. 

Met'. 

Met*. 

Met* 

Met?. 

0 

0.0000 

0.7645 

L5291 

2.2936 

3.0581 

322 

1.5872 

5.3517 

6.1163 

6.8808 

10 

- 

9.1711 

9.9389 

10.703 

11.468 

12.232 

12.997 

13.761 

H.5J-; 

20 

15.291 

16.055 

- 

17.585 

18.349 

19.114 

19.878 

20.643 

21.407 

22.172 

30 

22,936 

23.700 

24.455 

25.230 

26.759 

27.523 

29.052 

29.817 

40 

30.581 

31.345 

32.110 

32.875 

33.639 

34.404 

35.168 

35.933 

36.797 

37.462 

50 

:w.y.Hi 

" 

41.284 

42.049 

42.813 

43.578 

44.342 

45.107 

60 

15.872 

46.636 

•IT.lii] 

48.166 

49.695 

50.459 

51.224 

51.988 

52.753 

70 

53.517 

54.281 

55.W6 

55.811 

56.575 

57.::  m 

58.104 

58.869 

59.633 

60.398 

80 

61.163 

61.9-27 

62.69-2 

64.221 

64.986 

65.750 

66.515 

67.279 

68.044 

90 

,'.-..::- 

69.572 

"" 

71.102 

71. m,. 

73.395 

74.160 

74.924 

100 

76.453 

77.217 

78.747 

79.511 

80.276 

81.040 

81.805 

• 

83.:«4 

Conversion  of  Ci 

jbic  Metres 

Into 

Cubic 

Yards 

• 

Cubic  met 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Yds3. 

Yds*. 

Yds3. 

Yds:. 

Yds-. 

YdA 

1  .-  . 

Yds-. 

Yds;. 

Yd**. 

0 

0.0000 

1.3080 

2.6160 

6.5399 

7.8479 

9.1559 

10.464 

11.772 

10 

13.080 

14.388 

17.004 

18.313 

19.620 

20.928 

22.236 

23.544 

24.852 

20 

26.160 

27.468 

28.776 

30.084 

31.393 

32.700 

134.008 

35.316 

36.624 

37.932 

30 

39.240 

40.548 

41.856 

43.164 

44.473 

17.088 

48.396 

49.704 

51.012 

40 

52.319 

53.627 

54.935 

56.243 

57.552 

58.859 

60.167 

61.475 

62.783 

63.091 

50 

65.399 

66.707 

68.015 

69.323 

3 

71.939 

73.247 

74. .545 

75.863 

77.171 

60 

78.479 

79.787 

81.095 

82.403 

83.712 

85.019 

86.327 

87.535 

Sv913 

yi.-j.5i 

70 

91.559 

92.867 

94.175 

95.483 

96.792 

98.099 

99.407 

100.71 

102.02 

103.33 

80 

104.63 

105.94 

107.25 

108.56 

109.87 

111.17 

112.48 

113.79 

115.10 

116.41 

90 

117.72 

119.03 

120.34 

121.64 

122.95 

124.26 

125.57 

126.88 

128.18 

129.49 

100 

130.80 

132.11 

133.42 

134.72 

136.03 

137.34 

138.65 

139.96 

141.26 

142.57 

Conversion  of  U.  S.  Gallons  into  Litres. 


Gal  1 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Litres.  Litres. 

Litres. 

Litres. 

Litres. 

Litres. 

Litres, 

Litres. 

Litrea 

Litres, 

0 

0.0000  3.7853 

7.5706 

11.356 

15.141 

18.946 

22.712 

26.497 

30.282 

34.068 

10 

37.853:  41.6&8 

45.423 

49.209 

52.994 

56.799 

60.565 

64.350 

68.135 

71.921 

20 

75.706  79.491 

83.276 

87.062 

90.847 

94.652 

98.418 

102.20 

105.99 

109.77 

30 

113.50 

117.34 

121.13 

124.92 

128.66 

132.50 

136.27 

140.06 

143.84 

147.63 

40 

151.42 

155.  J  J 

158.99 

162.78 

166.56 

170.36 

174.13 

177.92 

181.70 

185.49 

50 

189.46 

193.24 

197.03 

200.82 

204.60 

208.40 

212.17 

215.96 

219.74 

223.53 

60 

227.12 

230.90 

234.69 

238.48 

242.26 

246.06 

249.83 

253.62 

257.40 

261.19 

70 

264.97 

268.75 

272.. 54 

276.33 

280.11 

283.91 

286.68 

291.47 

295.25 

299.04 

80 

302.82 

306.60 

310.39 

314.18 

317.96 

321.76 

324.53 

329.32 

333.10 

336.89 

90 

440.68 

444.46 

448.25 

452.04 

459.62 

463.39 

467.18 

470.96 

471.75 

100 

47-.:.::  182.31 

486.10 

789.89 

493.67 

497.47 

501.24 

505.03 

508.81 

512.60 

Conversion  of  Litres  into  U.  S.  Gallons. 


Litres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

0 

0.0000 

0.2642 

0.7925 

1.0567 

1.3209 

1.5851 

L8492 

2.1134 

2.3776 

10 

2.6418 

2.9060 

3.1702 

3.4343 

3.6985 

? 

4.2269 

4.4910 

4.7552 

5.0194 

. 

5.2836 

5.5478 

5.8120 

6.3403 

6.6045 

6.8687 

7.1328 

7.3970 

7.6612 

30 

7.9254 

8.1896 

8.717V 

8.9821 

9.2463 

9.5105 

9.8746 

: 

10.303 

40 

10.567 

1     - 

11.095 

11.624 

12.152 

12.416 

12.680 

12.945 

50 

13.473 

- 

14.002 

14.266 

14.530 

14.794 

15.058 

• 

15.587 

60 

- 

16.115 

16.644 

16.908 

17.172 

L7  1 

17.700 

70 

19.020 

• 

19.549 

19.813 

20.077 

20.341 

20.605 

20.870 

80 

21.134 

21.398 

21.662  21.926  22.191 

22. 155 

22.719 

22.983 

23.247 

23.512 

90 

24.040 

24.304  24.568  24  - 

25.097 

25.361 

25.625 

25.88  l 

26.154 

100 

■    i 

26.946  27.210  27.475 

27.739 

28.003 

1  2S.796 

500 


The  Metric  System:. 


Conversion  of  Yards 

nto  Metres 

Yards. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

0 

0.0000 

0.9144 

1.8288 

2.7432 

3.6576 

4.5719 

5.4863 

6.4007 

7.3151 

8.2295 

10 

9.1439 

10.058 

10.973 

11.887 

12.801 

13.716 

14.630 

15.544 

16.458 

17.373 

20 

18.288 

19.202 

20.117 

21.031 

21.945 

22.860 

23.774 

24.689 

25.603 

26.518 

30 

27.432 

28.346 

29.260 

30.174 

31.088 

32.003 

32.917 

33.832 

34.746 

35.661 

40 

36.576 

37.490 

38.404 

39.318 

40.232 

41.147 

42.061 

42.976 

43.890 

44.805 

50 

45.719 

46.634 

47.548 

48.462 

49.376 

50.291 

51.205 

52.120 

53.034 

53.949 

60 

54.863 

55.778 

56.692 

57.606 

58.520 

59.435 

60.349 

61.264 

62.178 

63.093 

70 

64.007 

64.922 

65.836 

66.750 

67.664 

68.578 

69.493 

70.408 

71.322 

72.237 

80 

73.151 

74.066 

74.980 

75.894 

76.808 

77.723 

78.637 

79.552 

80.466 

81.381 

90 

82.295 

83.210 

84.124 

85.038 

85.952 

86.867 

87.781 

88.696 

89.610 

90.525 

100 

91.439 

92.353 

93.267 

94.181 

95.095 

96.010 

96.924 

97.839 

98.753 

99.668 

Conversion  of  Metres 

into 

Vards. 

Metres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

0 

0.0000 

1.0936 

2.1872 

3.2809 

4.3745 

5.4081 

6.5617 

7.6553 

8.7490 

9.8426 

10 

10.936 

12.029 

13.122 

14.217 

15.310 

16.404 

17.498 

18.591 

19.685 

20.778 

20 

21.872 

22.966 

24.059 

25.153 

26.247 

27.340 

28.434 

29.527 

30.621 

31.715 

30 

32.809 

33.900 

34.993 

36.090 

37.184 

38.277 

39.371 

40.464 

41,558 

42.652 

40 

43.745 

44.839 

45.932 

47.026 

48.120 

49.213 

50.307 

51.400 

52.544 

53.588 

50 

54.681 

55.775 

56.868 

57.962 

59.056 

60.149 

61.243 

62.336 

63.430 

64.524 

60 

65.017 

66.711 

67.804 

6S.898 

69.992 

71.085 

72.179 

73.272 

74.366 

75.460 

70 

76.553 

77.647 

78.740 

79.834 

80.928 

82.021 

83.115 

84.208 

85.302 

86.396 

80 

87.490 

88.584 

89.677 

90.771 

91.865 

92.958 

94.052 

95.145 

96.239 

97.333 

90 

98.426 

99.520 

100.61 

101.71 

102.80 

103.89 

104.99 

106.08 

107.17 

108.27 

100 

109.36 

110.45 

111.55 

112.64 

113.73 

114.83 

115.92 

117.02 

118.11 

119.20 

Conversion 

of  Square  Y 

ards 

into  Square 

Metres. 

Sq.  yards. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Met2. 

Met-. 

Met2. 

Met?. 

Mel?. 

Met2. 

Met?. 

Met-'. 

Met?. 

Met-. 

0 

0.0000 

0.8361 

1.6722 

2.5803 

3.3444 

4.1805 

5.0167 

5.8528 

6.6889 

7.5250 

10 

8.3611 

9.1972 

10.033 

10.941 

11.706 

12.542 

13.378 

14.214 

15.050 

15.886 

20 

16.722 

17.558 

18.394 

19.102 

20.066 

20.903 

21.739 

22.575 

23.411 

24.247 

30 

25.083 

25.919 

26.755 

27.663 

28.431 

29.264 

30.100 

30.936 

31.772 

32.608 

40 

33.444 

34.280 

35.116 

36.024 

36.788 

37.625 

38.461 

39.297 

40.133 

40.969 

50 

41.805 

42.641 

43.477 

44.385 

45.149 

45.986 

46.822 

47.658 

48.494 

49.330 

60 

50.167 

51.003 

51.839 

52.747 

53.511 

54.348 

55.184 

56.020 

56.856 

57.692 

70 

58.528 

59.364 

60.190 

61.108 

61.872 

62.709 

63.545 

64.381 

65.217 

66.053 

80 

66.889 

67.725 

68.561 

69.469 

70.233 

71.070 

71.906 

72.742 

73.578 

74.414 

90 

75.250 

76.086 

76.922 

77.830 

78.594 

79.431 

80.267 

81.103 

81.939 

82.775 

100 

83.611 

84.447 

85.283 

86.191 

86.955 

87.792 

88.628 

89.464 

90.300 

91.136 

Conversion 

of  Square  Metres  into  Square  Yards. 

Sq.  metres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Yds2. 

Yds2. 

Yds-'. 

Yds2. 

Yds2. 

Yds2. 

Yds2. 

Yds2. 

Yds2. 

Yds2. 

0 

0.0000 

1.1960 

2.3920 

3.5880 

4.7840 

5.9800 

7.1760 

8.3720 

9.5681 

10.764 

10 

11.960 

13.156 

14.352 

15.548 

16.744 

17.940 

19.136 

20.332 

21.528 

22.724 

20 

23.920 

25.116 

26.312 

27.508 

28.704 

29.900 

31.096 

32.292 

33.488 

34.684 

30 

35.880 

37.076 

38.272 

39.468 

40.664 

41.860 

43.056 

44.252 

45.448 

46.644 

40 

47.840 

49.036 

50.232 

51.428 

52.624 

53.820 

55.016 

56.212 

57.408 

58.604 

50 

59.800 

60.996 

62.192 

63.388 

63.584 

65.780 

66.976 

68.172 

69.368 

70.564 

60 

71.760 

72.956 

74.152 

75.348 

76.544 

77.740 

78.936 

80.132 

81.328 

82.524 

70 

83.721 

84.917 

86.113 

87.309 

88.505 

89.701 

90.897 

92.093 

93.289 

94.485 

80 

95.681 

96.877 

98.073 

99.269 

100.46 

101.66 

102.86 

104.06 

105.25 

106.44 

90 

107.64 

108.84 

110.03 

111.24 

112.44 

113.62 

114.81 

116.01 

117.21 

118.40 

100 

119.60 

120.80 

121.99 

123.19 

124.38 

125.58 

126.77 

127.97 

129.17 

130.36 

Thk  Mf.tr  ic  System. 


601 


Conversion 

of  Hectares  into 

Acre* 

>. 

H>  i  ' 

o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Acres. 

Acres. 

Acres. 

Acres. 

Acres. 

Acres. 

Acres. 

Acres. 

0 

0.0000 

2.4711 

4.9422 

7.4133 

9  88  1 1 

12.355 

17.298 

19.769 

22.240 

10 

24.711 

27.182 

29.653 

32.124 

34.695 

37.046 

39.547 

42.009 

44.480 

■ 

20 

49.422 

51.893 

54.364 

56.835 

59.3(16 

61.757 

64.258 

66.720 

68.191 

71.662 

30 

74.133 

76.601 

79.075 

81.546 

84.017 

86.468 

88.969 

91.431 

93.902 

96.373 

40 

98.844 

101.31 

103.79 

106.26 

111.181 113.68 

116.14 

ll.s.  61 

121.08 

123.55 

126.02 

128.49 

130.96 

133.43 

135.88  138.38 

140.85 

143.32 

145.79 

1 18  36 

150.83 

" 

155.77 

158.24 

160.69  163.19 

165.66 

168.13 

170.60 

172.95 

175.45 

177.9-2 

180.39 

182.86 

185.31  187.81 

190.28 

192.75 

195.22 

- 

197  I  1 

200.16 

202.63 

205.10 

207.57 

210.02  212.52 

214.99 

217.16 

219.93 

90 

222.40 

224. S7 

227.34 

232.28 

234.78  237.23 

239.70 

242.17 

244.64 

100 

247.11 

249.58 

252.05 

254.52 

256.99 

259.44  261.91 

264.41 

266.88 

269.35 

Conversion  of  Acres  into  Hectares. 

A'  res. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Hect 

Hect. 

Hect 

Hect 

Ilect. 

Hect. 

Ilect. 

Hect. 

Hect 

Hect. 

0 

0.0000 

0.4047 

0.8093 

1.2140 

1.6187 

2.0234 

2.4280 

-  -  27 

3.2374 

3.6420 

10 

4.0468 

4.4515 

4.8561 

5.2608 

5.6655 

6.0702 

6.4748 

6.8795 

7.2782 

7.6888 

2 

8.0936 

8.4983 

8.9029 

9.3076 

9.7123 

10.117 

10.521 

10.926 

11.331 

11.735 

30 

12.140 

12.545 

12.949 

13.354 

13.759 

14.163 

14.568 

14.973 

15.377 

15.782 

40 

16.187 

- 

16.996 

17.401 

17.806 

18.210 

l.s.615 

19.020 

19.414 

19.829 

50 

20.234 

20.639 

21.043 

21.448 

21.853 

22.257 

22.662 

2:'..  (167 

23. 171 

23.876 

60 

24.280 

24.685 

25.089 

25.494 

25.899 

26.303 

26.708 

27.113 

27.517 

27.922 

70 

28.327 

28.732 

29.136 

29.541 

29.946 

30.&50 

30.7.55 

31.160 

31.564 

31.969 

80 

32.374 

32.779 

33.183 

33.588 

33.993 

34.397 

34.802 

35.207 

35.611 

36.016 

90 

36.420 

36.825 

37.220 

38.039 

38.443 

38.848 

39.253 

39.657 

40.062 

100 

40.46S 

40.873 

41.277 

41.682 

42.087 

42.491 

42.8% 

43.301 

43.695 

44.110 

Conversion  of 

Square  M: 

'es  inf 

o  Square  K 

iiometres. 

Bq.  miles. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 

KiP. 

0.0000 

25.899 

51.798 

77.697 

103.59 

129.29 

1 

181.29 

207.19 

233.09 

258.99 

Kil*. 

54.388 
-     287 
106.18 
131.88 

1 
:-    -- 

209.77 
235.68 
261.58 

KiP. 

5.1798 

31.079 
56.978 
82.877 
108.77 
134.47 
160.57 
186.47 
212.36 
238.27 
264.17 

Kil-'. 

7.7697 
33.669 
59.568 
85.467 
111.36 
137.06 
163.16 

214.95 
240.86 
266.76 

Kil-'. 

10.359 
36.259 
62.158 
88.057 
113.95 
139.65 
165. 7.". 
191.65 
217.55 
243.45 
269.35 

Kil-'. 

12.929 

38.829 
64.728 
90.627 
116.52 
142.22 
168.32 
194.22 
220.11 
246.02 
271.92 

Kil-!. 

15.539 
41.439 

93.238 

119.13 
144.83 

170.93 
196.83 
222.73 
248.63 

271.r,:: 

Kil-'. 

18.129 

44.029 
- 
96.828 
121.72 
147.42 
173.52 
199.42 
225.31 
251  22 
277!l2 

Kil-1. 

20.718 
46.619 
72.. Ms 
98.417 
124.31 
150.01 
176.11 
202.01 
227.91 
2?    •: 
279.71 

KU*. 

23.309 
49.209 
75.108 
101.01 
126.90 
152.50 
178.70 
204.60 
230.50 
2.56.40 
282.20 

Cc 

inversion  of  Square  Kil 

ometres  int 

o  Square  Miles. 

Bq.  kil"m. 

0 

1 

2 

3 

4 

5          6 

7 

8 

9 

Sq.  m. 

Sq.  m. 

Bq.  in. 

Sq.  m.  Sq.  m. 

Sq.  ni.  Sq.  m. 

Sq.  m 

Sq.  m. 

Sq.  m. 

0 

0.0000 

0.3861 

0.772-2 

1.1583  1.5445 

1.9304  2.3166 

2.7028 

3,1719 

10 

1.8612 

1.2171 

4.6334 

(.4057 

5.7916  6.1778 

6.5640 

6.9.502 

" 

20 

:  7224 

8.1081 

8.4946 

3.8807  9.2669 

_'S    1O.030 

10.425 

10.811 

11.197 

30 

11.583 

11.969 

1 

12.741 

13.127 

13.513  13.899 

14.286 

14.672 

15.058 

40 

15.445 

16.217 

16.603 

16.9V.' 

17.3,75  17.761 

18.146 

18.534 

18.920 

50 

19.304 

19.691 

20.076 

20.848 

21.231  21 

22.007 

22.303 

22.779 

60 

23.166 

23.93* 

24.324 

21.710 

25.096 

25.482 

25.869 

26.245 

26.641 

Tii 

27.028 

27.413 

27.800 

28.186 

28.958 

29.344 

29.731 

30.117 

80.503 

80 

30.890 

31.274 

81.662 

32.048 

33.979 

90 

31.749 

35.135 

36.679 

37.065 

37.452 

-   - 

38.224 

100 

38.612  38.996 

•    -  1 

39.770 

10.156 

2  10.928 

41.315 

11.701 

i 

502 


The  Metric  System:. 


Conversion 

of  Cubic  Feet  into  Cub 

c  Decimetres. 

Cubic  feet. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Dml 

Din3. 

Dm3. 

Dml 

Dm3. 

Dm3. 

Dm3. 

Dm3. 

Dml 

Dm3. 

0 

0.0000 

28.316 

56.632 

84.948 

113.26 

141.58 

169.90 

198.21 

226.53 

254.84 

10 

283.16 

311.47 

339.79 

268.11 

396.42 

424.74 

453.06 

481.37 

509.69 

538.00 

20 

566.32 

594.64 

622.95 

651.27 

679.58 

707.90 

736.22 

764.53 

792.85 

821.16 

30 

849.48 

877.80 

906.11 

934.43 

962.74 

991.06 

1019.4 

1047.7 

1076.0 

1104.3 

40 

1132.6 

1160.8 

1189.2 

1217.5 

1245.9 

1274.2 

1302.5 

1330.8 

1359.1 

1387.4 

50 

1415.8 

1444.0 

1472.4 

1500.7 

1529.1 

1557.4 

1585.7 

1614.0 

1642.3 

1670.6 

60 

1698.9 

1727.2 

1755.5 

1783.8 

1812.2 

1840.5 

1868.8 

1897.1 

1925.4 

1953.7 

70 

1982.1 

2010.3 

2038.7 

2067.0 

2095.4 

2123.7 

2152.0 

2180.3 

2208.6 

2236.9 

80 

2265.3 

2293.5 

2321.9 

2350.2 

.2378.6 

2406.9 

2435.2 

2163.5 

2491.8 

2520.1 

90 

2548.4 

2576.6 

2605.0 

2633.3 

2661.6 

2690.0 

2718.3 

2746.6 

2774.9 

2803.2 

100 

2831.6 

2859.8 

2888.2 

2916.5 

2944.9 

2973.2 

3001.5 

3029.8 

3058.1 

3086.4 

Conversion 

of  Cubic  Decimetres  into  Cubic  Feet. 

Cubic  dm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Ft3. 

Ft3. 

Ft3. 

Ft3. 

Ft3. 

Ft3. 

Ft3. 

Ft3. 

Ft3. 

Ft3. 

0 

0.0000 

0.0353 

0.0706 

0.1059 

0.1413 

0.1766 

0.2119 

0.2472 

0.2825 

0.3178 

10 

0.3531 

0.3884 

0.4237 

0.4590 

0.4944 

0.5297 

0.5540 

0.6003 

0.6356 

0.6709 

20 

0.7063 

0.7416 

0.7766 

0.8122 

0.8476 

0.8829 

0.9182 

0.9535 

0.9888 

1.0241 

30 

1.0594 

1.0947 

1.1300 

1.1653 

1.2007 

1.2360 

1.2713 

1.3066 

1.3419 

1.3772 

40 

1.4126 

1.4479 

1.4832 

1.5185 

1.5539 

1.5892 

1.6245 

1.6608 

1.6951 

1.7304 

50 

1.7658 

1.8011 

1.8364 

1.8717 

1.9071 

1.9424 

1.9777 

2.0130 

2.0483 

2.0836 

60 

2.1189 

2.1542 

2.1895 

2.2248 

2.2602 

2.2955 

2.3308 

2.3661 

2.4014 

2.4367 

70 

2.4721 

2.5074 

2.5427 

2.5780 

2.6134 

2.6487 

2.6840 

2.7193 

2.7546 

2.7899 

80 

2.8252 

2.8605 

2.8958 

2.9311 

2.9665 

3.0018 

3.0371 

3.0724 

3.1077 

3.1430 

90 

3.1784 

3.2137 

3.2490 

3.2843 

3.3197 

3.3550 

3.3903 

3.4256 

3.4609 

3.4962 

100 

3.5315 

3.5668 

3.6021 

3.6374 

3.6728 

3.7081 

3.7434 

3.7787 

3.8140 

3.8493 

Pounds  per  Square  Foot  into  Kilogrammes  per  Square  Metre. 


Lbs.  pr  ft?. 


0 

10 
20 
30 
40 
50 
60 
70 
80 
90 
100 


0 


1 


K.  m2.  k.  m2. 


0.0000 
48.825 
97.650 
146.47 
195.30 
244.13 
292.95 
341.77 
390.06 
439.43 
488.25 


4.8825 
53.707 
102.53 
151.35 
200.13 
249.01 
297.83 
346.65 
394.94 
444.31 
493.13 


K.  m2.  K.  m2. 


9.7650 
58.590 
107.41 
156.23 
205.06 
253.89 
302.71 
351.53 
399.82 
449.19 
498.01 


14.647 

63.472 
112.30 
161.12 
209.95 
258.78 
307.60 
356.42 
404.71 
454.08 
502.90 


K.  m2. 

19.530 
68.355 
117.18 
165.90 
214.83 
263.66 
312.48 
361.20 
409.59 
458.96 
507.78 


K.m2. 

24.413 
73.238 
122.06 
170.88 
219.71 
268.54 
317.36 
366.18 
414.47 
463.34 
512.66 


K.  m2. 

29.295 
78.120 
126.94 
175.76 
224.59 
273.42 
322.24 
371.06 
419.35 
468.72 
517.54 


K.  m2. 

34.177 

83.002 
131.83 
180.65 
229.48 
278.31 
327.13 
375.95 
424.24 
473.61 
522.43 


8 


K.m2. 

39.006 
87.831 
136.66 
185.47 
234.30 
283.13 
331.95 
880.77 
429.06 
478.43 
527.25 


K.  m2. 

43.943 
92.768 
141.59 
190.41 
239.24 
288.08 
336.89 
385.71 
434.00 
483.37 
532.19 


Kilogra 

mmes 

per  Square  Metre  into  Pounds  per  Square  Foot. 

K.  per  m2. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Lb.  ft? 

Lb.  ft? 

Lb.  ft2 

Lb.  ft2 

Lb.  ft2 

Lb.  m 

Lb.  ft2  Lb.  ft2 

Lb.  ft2 

Lb.  ft2 

0 

0.0000 

0.2048 

0.4096 

0.6144 

0.8192 

1.0240 

1.2289 

1.4337 

1.6385 

1.8433 

10 

2.0481 

2.2529 

2.4577 

2.6625 

2.8673 

3.0721 

3.2770 

3.4818 

3.6866 

3.8914 

20 

4.0962 

4.3010 

4.5058 

4.7106 

4.9154 

5.1202 

5.3251 

5.5299 

5.7347 

5.9395 

30 

6.1444 

6.3492 

6.5540 

6.7588 

6.9636 

7.1684 

7.3733 

7.5781 

7.7829 

7.9877 

40 

8.1925 

8.3973 

8.6021 

8.8069 

9.0117 

9.2165 

9.4214 

9.6262 

9.8310 

10.036 

50 

10.240 

10.445 

10.649 

10.854 

11.059 

11.264 

11.469 

11.674 

11.878 

12.083 

60 

12.289 

12.494 

12.698 

12.903 

13.108 

13.313 

13.518 

13.723 

13.927 

14.132 

70 

14.337 

14.542 

14.746 

14.951 

15.156 

15.361 

15.566 

15.771 

15.975 

16.180 

80 

16.385 

16.590 

16.794 

16.999 

17.204 

17.409 

17.614 

17.819 

18.023 

18.228 

90 

18.433 

18.638 

18.842 

19.047 

19.252 

19.457 

19.662 

19.867 

20.071 

20.276 

100 

20.481 

20.686 

20.890 

21.095 

21.300 

21.505 

21.710 

21.915 

22.119 

22.324 

Tun  MnTr.ic  System. 


503 


Pc 

unds 

per  Square 

Inch 

nto  Atmospheric 

Pressure. 

Lbe.  pr  in2. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

At. 

At. 

At. 

At. 

At. 

At. 

At. 

At. 

At. 

At. 

0 

0.0000 

0.1361 

0.2041 

0.2722 

0.3402 

0.  1763 

0.5443 

0.6124 

10 

0.6804 

M.71M 

0.8165 

0.8845 

1.0206 

1.1567 

1.2247 

1.2928 

2D 

1.3608 

1.4288 

1.4969 

1.5649 

: 

1.7010 

1.7690 

1.9051 

1.9732 

30 

2.0413 

2.1093 

2.1771 

2. 'JIM 

2.3135 

2.381 1 

2.4  l'J"> 

2.5176 

2.6537 

40 

2.7217 

2.7897 

2.n»7> 

2.9258 

. 

3.0619 

:;.12'".» 

3.19H) 

3.2660 

3.3341 

50 

3.4021 

3.4701 

3.6743 

3.7423 

3.8103 

3.8784 

3.9464 

4.0145 

60 

1    -. 

4.1505 

4.2186 

4.::'.  17 

4.4227 

4.4907 

1 

1.6268 

4.6949 

70 

:  " 

4.8991 

1.9671 

5.0352 

5.1031 

5.1712 

5.2393 

5.3073 

5.3754 

80 

5.4434 

5.5114 

5.5795 

f>.r.i7."> 

5.7156 

5.7836 

5.8516 

5.9197 

5.9877 

6.0558 

6.1238 

6.191* 

6.2599 

6.3279 

6.3960 

6.4640 

■ 

6.6001 

6.6681 

6.7362 

100 

6.8042 

6  8722 

6.9403 

7.0083 

J 

7.1111 

7.2121 

; 

7.3485 

7.4166 

Atmospheric 

Pressure  into  Pot 

inds  per  Sq 

uare  1 

nch. 

A tm.  pre*. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Lb.  in? 

Lb.  in? 

Lb.  in? 

Lb.in- 

Lb.  in? 

Lb.  in? 

Lb.in? 

Lb.in2 

Lb.  in-' 

Lb.in2 

0 

0.0000 

11.697 

44.090 

58.787 

73.483 

8<.l*  i 

102.87 

117.57 

132.27 

10 

146.97 

161.67 

176.36 

191.06 

205.76 

220.45 

235.15 

249.84 

264.54 

279.24 

20 

293.93 

308.63 

323.32 

338.02 

352.72 

367.41 

382.11 

396.80 

411.50 

426.20 

30 

440.90 

455.60 

470.29 

484.99 

499.69 

514.38 

529.08 

543.77 

558. 17 

573.17 

40 

587.87 

617.26 

631.96 

646.66 

661.35 

676.05 

690.74 

705.44 

720.14 

50 

734.83 

749.53 

764.22 

778.92 

793.62 

808.31 

823.01 

837.70 

852.40 

867.10 

60 

>M>0 

896.50 

911.19 

925.89 

940.59 

955.28 

969.98 

984.67 

999.37 

1014.1 

70 

1028.7 

1043.4 

10.58.1 

1072.8 

1087.5 

1102.2 

1116.9 

1131.6 

1146.3 

1161.0 

80 

1175.7 

1190.4 

1205.1 

1219.8 

1234.5 

1249.2 

1263.9 

1278.6 

1293.3 

1308.0 

90 

1322.7 

1337.4 

1352.1 

1366.8 

1381.5 

1396.2 

1410.9 

1425.6 

1439.3 

1455.0 

100 

1469.7 

1484.4  1499.1 

1513.8 

1528.5 

1543.2 

1557.9 

1572.6 

1586.3 

1602.0 

Pounds  per  Square  I 

nch  in 

to  Kil 

ogrammes 

per  Sq 

uare 

Centimetre. 

Lbs.  prin-. 

0           1 

2 

3 

4 

5 

6 

7 

8 

9 

K.cni?  K.cni? 

K.cni? 

K.em? 

K.cm? 

K.cni? 

K.em? 

K.cni? 

K.cm? 

K.cm2 

0 

0.0000  0.0703 

0.1406 

0.2109 

0.2S12 

0.3515 

0.4218 

0.4921 

0.5625 

0.6328 

10 

0.7031  0.77    1 

0.8437 

0.9140 

0.9843 

1.0.546 

1.1249 

1.1952 

1.2655 

1.3358 

20 

1.4062  L4765 

1.546S 

1.6171 

1.6874 

1.7577 

1.8280 

1.8983 

1.96Mi 

2.0389 

30 

2.1092  2.1795 

2.2498 

2.3202 

2.3905 

2.4608 

2.5311 

2.6014 

2.6717 

2.7420 

40 

2.8123  2.8826 

2.9529 

3.0232 

3.0935 

3.1639 

3. 23 12 

3.3045 

3.3748 

3.4451 

50 

3.5151  3.       " 

3.6560 

3.7263 

3.7966 

3.8669 

3.9372 

4.0075 

4.0779 

4.1482 

60 

4.2185  4.2888 

4.3591 

4.4294 

4.4997 

4.5700 

4.6403 

4.7106 

4.7809 

4.8512 

70 

4.9216  4.9919 

5.0622 

5.1325 

5.2028 

5.2731 

5.3434 

5.4137 

5.4840 

5.5543 

80 

5.6246  5.6949 

5.7652 

5.8356 

5.9059 

5.9762 

6.0465 

6.1168 

6.1871 

6.2574 

90 

6.3277' 6.39*0 

6.4683 

6.5386 

6.6089 

6.6793 

6.7496 

6.8199 

6.8902 

6.9605 

100 

7.0308  7.1011 

7.1714 

7.2117 

7.3120 

7.3823 

7.4526 

7.5229 

7.5933 

7.6636 

Kilogrammes  per  Square  Centimetre  into  Pounds  per  Square  Inch. 


K.  per  cm2. 

0 

1           2 

3 

4 

5 

6 

7          8 

9 

Lb.  in? 

Lb. in-  Lb. in? 

Lb.  in? 

Lb.in? 

Lb.  in? 

Lb.  in? 

Lb. in?  Lb. in2 

Lb.  in2 

0 

0.0000 

11.22:;  28.446 

12.670 

56.893 

71.116 

- 

99.562. 113.78 

128.01 

10 

1 12.23 

156.45  17 

184.90 

199.12 

213.35 

227.57 

241. 79 '  256.02 

270.24 

20 

298.69  312.91 

327.13 

34L36 

355. 5* 

369.80|  384.031 398.25 

412.47 

30 

126.70 

440.92  455.14 

;-      • 

497.81 

512.03  526.26  540.48  554.70 

40 

.568.93 

583.1".  5 

611.60 

640.04 

654.27  668.49  682.71 

696.94 

50 

711.16 

725.!      J 

3      - 

768.05 

782.28 

796.50  810.72  S24.94 

839.17 

60 

853.39 

867.61   B81.84 

896.06 

910.28 

7.18 

981.40 

70 

995.62 

1009.S  1024.1 

:     - 

• 

1066.7 

1081.0  1095.2  1109.4 

1123.6 

80 

1137.8 

1152.1  1166.3 

1180.5 

1194.7 

1209.0 

1223.2 

.4,1251.6 

1265.9 

90 

1280.1 

1294.3  1308.5 

1322.7 

1337.0 

1  61.2 

.1 

1379.6  1 

1408.1 

100 

1422.3 

1436.5  1450.8 

1465.0 

1 179.2  1  1 

1507.7  1521.9  1536.1    1 

504 


Tim  Metric  System". 


c 

Conversion  of  English  Pounds  into 

Kilog 

rammes. 

Eug.  lbs. 

0 
Kilo. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

0 

0.000 

0.453 

0.907 

1.361 

1.814 

2.26S 

2.722 

3.175 

3.629 

4.082 

10 

4.536 

4.989 

5.443 

5.897 

6.350 

6.804 

7.258 

7.711 

8.165 

8.618 

20 

9.072 

9.525 

9.979 

10.43 

10.89 

11.34 

11.79 

12.25 

12.70 

13.15 

30 

13.61 

14.06 

14.52 

14.97 

15.42 

15.88 

16.33 

16.78 

17.24 

17.69 

40 

18.11 

18.59 

19.05 

19.50 

19.95 

20.41 

20.86 

21.31 

21.77 

q.>  22 

50 

22.6s 

23.13 

23.59 

24.04 

24.49 

24.95 

25.40 

25.85 

26.31 

26.76 

60 

27.22 

27.67 

28.13 

28.58 

29.03 

29.49 

29.94 

30.39 

30.85 

31.30 

70 

31.75 

32.20 

32.66 

33.11 

38.56 

34.02 

34.47 

34.92 

35.38 

35.83 

80 

36.29 

36.74 

37.20 

37.65 

38.10 

38.56 

39.01 

39.46 

39.92 

40.37 

90 

40.82 

41.27 

41.73 

42.18 

42.63 

43.09 

43.. 54 

43.99 

44.45 

44.90 

100 

45.36 

45.81 

46.27 

46.72 

47.17 

47.63 

48.08 

48.53 

48.99 

49.44 

Conversion  < 

>f  Kilogram 

mes  i 

ito  English 

Poun 

ds. 

Fr.  kilo. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

0 

0.000 

2.205 

4.410 

6.615 

8.820 

11.02 

13.23 

15.43 

17.64 

19.84 

10 

22.05 

24.25 

26.46 

28.67 

30.87 

33.07 

35.28 

37.48 

39.69 

41.89 

20 

44.10 

46.30 

48.51 

50.72 

52.92 

55.12 

57.33 

59.53 

61.74 

63.94 

30 

66.15 

68.35 

70.56 

72.77 

74.97 

77.17 

79.38 

81.58 

83.79 

85.99 

40 

88.20 

90.40 

92.61 

94.82 

97.02 

99.22 

101.4 

103.6 

105.8 

108.0 

50 

110.2 

112.5 

114.6 

116.8 

119.0 

121.2 

123.4 

125.6 

127.8 

130.0 

60 

132.3 

134.5 

136.7 

138.9 

141.1 

143.3 

145.5 

147.7 

149.9 

152.1 

70 

154.3 

156.5 

158.7 

160.9 

163.1 

165.3 

167.5 

169.7 

171.9 

174.1 

80 

176.4 

178.6 

180.8 

183.0 

185.2 

187.4 

189.6 

191.8 

194.0 

196.2 

90 

198.4 

200.6 

202.8 

205.0 

207.2 

209.4 

211.6 

213.8 

216.0 

218.2 

100 

220.5 

222.7 

224.9 

227.1 

229.3 

231.5 

233.7 

235.9 

238.1 

240.3 

Conversion  of  Ei 

iglish  Tons 

into 

Metric  Tons 

• 

Eng.  tons. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

M.ton 

M.ton 

M.ton 

M.  ton 

M.  ton 

M.ton 

M.ton 

M.ton 

M.ton 

M.  ton 

0 

0.000 

1.016 

2.032 

3.048 

4.064 

5.080 

6.096 

7.112 

8.128 

9.144 

10 

10.16 

11.18 

12.19 

13.21 

14.12 

15.21 

16.26 

17.27 

18.29 

19.30 

20 

20.32 

21.34 

22.35 

23.37 

24.38 

25.40 

26.42 

27.43 

28.45 

29.46 

30 

30.48 

31.50 

32.51 

33.53 

34.54 

35.56 

36.58 

37.59 

38.61 

39.62 

40 

40.64 

41.66 

42.67 

43.69 

44.70 

45.74 

46.74 

47.75 

48.77 

49.78 

50 

50.80 

51.82 

52.83 

53.85 

54.86 

55.88 

56.90 

57.90 

58.93 

59.94 

60 

60.96 

61.97 

62.99 

64.01 

65.02 

66.04 

67.06 

68.07 

69.09 

70.10 

70 

71.12 

72.14 

73.15 

74.17 

75.18 

76.20 

77.22 

78.23 

79.25 

80.26 

80 

81.28 

82.29 

83.31 

84.33 

85.34 

86.36 

87.38 

88.39 

89.41 

90.42 

90 

91.44 

92.46 

93.47 

94.49 

95.50 

96.52 

97.54 

98.55 

99.57 

100.6 

100 

101.6 

102.6 

103.6 

104.6 

105.7 

106.7 

107.7 

108.7 

109.7 

110.7 

Conversion  of  Metric  Tons  into  English  Tons. 


Fr.  m.  ton. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

0 

0.000 

0.984 

1.969 

2.953 

3.937 

4.921 

5.906 

6.890 

7.874 

8.858 

10 

9.843 

10.83 

11.81 

12.79 

13.78 

14.76 

15.75 

16.73 

17.72 

18.70 

20 

19.69 

20.67 

21.66 

22.64 

23.63 

24.61 

25.60 

26.58 

27.56 

28.55 

30 

29.53 

30.51 

31.50 

32.48 

33.47 

34.45 

35.44 

36.42 

37.40 

38.39 

40 

39.37 

40.35 

41.34 

42.32 

43.31 

44.29 

45.28 

46.26 

47.24 

48.23 

50 

49.21 

50.19 

51.18 

52.16 

53.15 

54.13 

55.12 

56.10 

57.08 

58.07 

60 

59.06 

60.04 

61.03 

62.01 

63.00 

63.98 

64.97 

65.95 

66.93 

67.92 

70 

68.90 

69.88 

70.87 

71.85 

72.84 

73.82 

74.81 

75.79 

76.77 

77.76 

80 

78.74 

79.72 

80.71 

81.69 

82.68 

83.66 

84.65 

85.63 

86.61 

87.60 

90 

88.58 

89.56 

90.55 

91.53 

92.52 

93.50 

94.49 

95.47 

96.45 

97.44 

100 

98.43 

99.41 

100.4 

101.4 

102.4 

103.3 

104.3 

105.3 

106.3 

107.3 

The  Metric  System. 


505 


Conversion  of  English  Ounces  Avoirdupois  into  French  Grammes. 


Eujr.  ozs. 

0 

1 

2          3 

4 

5 

6 

7 

8 

9 

Grams  Grams 

Grams  Grams 

Grams 

Grams 

Grams  Grams 

Grams 

Grama 

0 

0.000"  28.348 

56.697  85.046 

113.39 

141.74 

170.09  198  U 

226.79 

255.14 

10 

283.4*  311. s:5 

340.18  368.52 

396.87 

425.22 

453.57  481.92 

510.27 

538.62 

20 

566.9715.' 

623.67  652.01 

680.36 

708.71 

737.06 

765.41 

793.76 

822.11 

30 

850.46  878  81 

907.16  9:55.50 

963.S5 

992.20 

1020.5 

1048.9 

1077.2 

1105.6 

40 

1133.9  1162.2 

1190.6  1218.9 

1247.3 

1275.6 

1304.0 

1332.8  1:560.7 

1389.0 

50 

1417.4  1445.7 

1171.1  1502.4 

153,0.8 

1559.1 

1587.5 

1615.8!  1644.2 

1672.5 

60 

1700.9  1729.2 

1756.6  17*5.9 

1814.8 

1842,9 

1871.0J  1899.3!  1927.7 

1956.0 

70 

1984.4;  2012.7 

2041.1  2079.4 

2097.8 

2126.1 

2154.5  21S2.8  2211.2 

2239.5 

80 

2267.9  2296.2 

2324.6  2352.9 

2381.8 

2409.6 

2438.0  2466.3  2494.7 

2523.0 

90 

2551.4  2579.7 

2608.1  2636.4 

2664.8 

2693.1 

2721.5  2739.8 

2778.2 

2806.5 

100 

2834.8  2863.1 

2*91. 5j  2919.8 

2948.2 

2976.5 

3004.9  3033.2;  3061.6 

3089.9 

Conversion  of  French  Grammes 

Into  English  Ounces  A 

voirdupois. 

Fr.  grams. 

o 

■ 

2 

3 

4 

5 

6 

7 

8 

9 

Ozs. 

Ozs. 

1  >/>. 

Ozs. 

Ozs. 

Ozs. 

Ozs. 

Ozs. 

Oza. 

Ozs. 

0 

0.0000 

0.0353 

0.0705 

0.1058 

0.1411 

0.1768 

0.2116 

0.2469 

0.2822 

0.3175 

10 

0.3527 

0.3**0 

0.4232 

0.15*5 

0.4938 

0.5295 

0.5643 

0.5996 

0.6349 

0.6702 

20 

0.7055  0.7408 

0.7760 

0.8113 

0.8466 

0.8823 

0.9171 

0.9524 

0.9877 

1.0230 

30 

1.0582  1.0935 

1.1287 

1.1640 

1.1993 

1.23.50 

1.2698 

1.3051 

1.3404 

1.3757 

40 

1.4110  1.4463 

1.4815 

1.5168 

1.5521 

1.5878 

1.6226 

1.6579 

1.6932 

1.7285 

50 

1.76-7 

L.8  'I  ' 

- 

1.8745 

1.9098 

1.9155 

1.9803 

2.01.56 

2.0509 

2.0862 

60 

2.1165 

2.1518 

2.1870 

2.2223 

2.2576 

2.2933 

2.3281 

2.3634 

2.3987 

2.43,10 

70 

2.4692 

2.5045 

2,5397 

2.5750 

2.6103 

2.6460 

2.6808 

2.7161 

2.7514 

2.7867 

80 

J  322 

2., 8-573 

2.8925 

2.9278 

2.9631 

2.9988 

3.0336 

3.0689 

3.1042 

3.1395 

90 

3.1717 

3.2100 

3.2452 

3.2805 

3.3158 

3.3515 

3.3863 

3.4216 

3.4.569 

3.4922 

100 

3.5275 

3.5628 

3.5ysi| 

3.6333 

3.6686 

3.7043 

3.7391 

3.7744 

3.8097 

3.8450 

Conversion  of  English  Grains  Troy  into  French  Grammes. 


Eng.  grains 

0          1 

2 

3 

4 

5 

6 

7 

8 

9 

Grams  Grams  Grams 

Grams 

Grams 

Grams 

Grams 

Grams 

Grams 

Grams 

0 

0.0000 

0.064S 

0.1296 

0.1944 

0.259-2 

0.3240 

0.3888 

0.4535 

0.5183 

0.5831 

10 

0.6479 

0.7127 

0.7775 

0.8423 

0.9071 

0.9719 

1.0367 

1.1014 

1.1662 

1.2310 

20 

1.2959 

1.3607 

1.4255 

1.4903 

1.5551 

1.6199 

1.6847 

1.7494 

1.8142 

1.8890 

30 

1.9438 

2.0086 

2.U73.1 

2.1382 

2.2030 

2.2678 

2.3326 

2.3973 

2.4621 

2.5269 

40 

2.5918 

2.6566 

2.7214 

2.7*62 

2.8510 

2.9158 

2.9806 

3.0453 

3.1101 

3.1749 

50 

3.2398 

3.3046 

3.3691 

3.4342 

3.4990 

3.5638 

3.6933 

3.7581 

3.8229 

60 

3.8877 

3.9525 

4.IH73 

4.0821 

4.1469 

4.2117 

4.2765 

4.3412 

4.4060 

4.4708 

70 

4.5357 

4.6005 

4.6653 

4.7301 

4.7919 

4.8597 

4.9245 

4.9892 

5.0540 

5.1188 

80 

5.1830 

5.2484 

5.3,132 

5.3780 

5.4428 

5.5076 

5.5724 

5.6371 

5.7019 

5.7667 

90 

5.8316 

5.8964 

5.9612 

6.0260 

6.0908 

6.15-56 

6.2204 

6.2.*:.l 

6.3499 

6.4147 

100 

6.4795 

6.5443 

6.6091 

6.6739 

6.7387 

6.8035 

6.8683 

6.9330 

6.997* 

7.0626 

Conversion  of  French  Grammes  into  English  Grains  Troy. 


Fr.  grams. 

0 

1 

Grs. 

Grs. 

0 

0.0000 

15.433 

10 

154.33 

169.76 

20 

308.66 

324.09 

30 

462.99 

178.42 

40 

617.65 

50 

771.65 

787.08 

60 

925.99 

941.42 

70 

1080.3 

1095.7 

80 

1234.6 

1250.0 

90 

1389.0 

1404.4 

100 

1543.3 

Grs, 
30.866 

1*5.19 
339.52 
493.86 

6  is. is 

802.52 
966.85 

1111.2 
1265  5 

1419.S 
1574.1 


* 


Grs. 

46.299 

200.63! 

354.96 

.509.29 

663.95 

817.95 

972.29 

1126.6 

1280.1 

1 135.31 

1589.6 


Grs.   I   Grs.      Grs,      Grs. 


61.732 
216.06 
370.39 

521.72 
679.3.* 
- 

1142.0 

12%.  3 
1450.7 
1605.0 


77.165 
231.49 
385.82 
510.15 
694231 
848.82 
1003.1 
1157.5 
1311.8 
1466.1 
1620.4 


92.599 

216.93 
401.26! 
555.59 
709.92 ' 
864.25 
1018.6 

1172.9 
1327.2 

1481.6 
1635.9 


Grs.      Grs. 


108.03 

262.36 
416.69 

571.02 
725.35 

879.68 
1034.0, 

11**.  3 

1342.6 

1  197.0 
1651.3 


125.46 
277.79 
432.12 
586.45 
740.78 
895.11 
1049.4 
L203.7 

• 
1-12.1 
16*36.7 


138  90 

2 

447.56 

601.89 

756.22 

910.55 

1064.9 

1219.2 

1373.5 

1527.9 

11  82.2 


506 


The  Metric  System. 


Horse-power  into  ChevaUvapeur. 


H. -power. 


0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 


0 

1 

2 

3 

4 

5 

6 

7 

8 

C.-v. 

0.0000 
10.136 
20.272 
30.408 
40.544 
50.680 
60.816 
70.952 
81.088 
91.224 
101.36 

C.-v. 

1.0136 
11.150 
21.308 
31.422 
41.557 
51.693 
61.829 
71.965 
82.102 
92.338 
102.37 

C.-v. 

2.0272 
12.163 
22.299 
32.435 
42.571 
52.707 
62.843 
72.979 
83.115 
93.251 
103.30 

C.-v. 

3.0408 
13.176 
23.313 
33.449 
43.585 
53.721 
63.857 
73.993 
84.129 
94.265 
104.40 

C.-v. 

4.0544 
14.190 
24.326 
34.462 
44.598 
54.734 
64.870 
75.006 
85.142 
95.278 
105.41 

C.-v. 

5.0680 
15.204 
25.240 
35.476 
45.612 
55.748 
65.884 
76.020 
86.156 
96.292 
106.43 

C.-v. 

6.0816 
16.218 
26.354 
36.490 
46.626 
56  762 
66.898 
77.034 
87.170 
97.306 
107.44 

C.-v. 

7.0952 
17.231 
27.367 
37.503 
47.639 
57.775 
67.911 
78.047 
88.183 
98.319 
108.45 

C.-v. 

8.1088 
18.245 
28.381 
38.517 
48.653 
58.789 
68.925 
79.061 
89.197 
99.333 
109.47 

C.-v. 

9.1224 
19.258 
29.394 
39.530 
49.666 
59.802 
69.938 
80.074 
90.210 
100.34 
110.48 


ChevaUvapeur  i 

nto  H 

orse=power 

I 

Chev.-vap. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

0 

0.0000 

0.9863 

1.9726 

2.9589 

3.9452 

4.9315 

5.9178 

6.9041 

7.8904 

8.8767 

10 

9.8630 

10.849 

11.835 

12.822 

13.808 

14.794 

15.781 

16.767 

17.753 

18.739 

20 

19.726 

20.712 

21.698 

22.685 

23.671 

24.657 

25.644 

26.630 

27.616 

28.602 

30 

29.589 

30.575 

31.561 

32.548 

33.534 

34.520 

35.507 

36.493 

37.479 

38.465 

40 

39.452 

40.438 

41.424 

42.411 

43.397 

44.383 

45.370 

46.356 

47.342 

48.328 

50 

49.315 

50.301 

51.287 

52.274 

53.260 

54.246 

55.233 

56.219 

57.205 

58.191 

60 

59.178 

60.164 

61.150 

62.137 

63.123 

64.109 

65.096 

66.082 

67.068 

68.054 

70 

69.041 

70.027 

71.013 

71.990 

72.986 

73.972 

74.959 

75.945 

76.941 

77.917 

80 

78.904 

79.890 

80.876 

81.863 

82.849 

83.835 

84.822 

85.808 

86.794 

87.780 

90 

88.767 

89.753 

90.739 

91.726 

92.712 

93.698 

94.785 

95.671 

96.657 

97.643 

100 

98.630 

99.616 

100.60 

101.59 

102.57 

103.56 

104.55 

105.53 

106.52 

107.50 

Foot=pounds  into  Kilogrammetres. 


Foot-lbs. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

0 

0.0000 

0.1382 

0.2764 

0.4146 

0.5528 

0.6910 

0.8292 

0.9674: 1.1056 

1.2438 

10 

1.3820 

1.5202 

1.6584 

1.7966 

1.9348 

2.0731 

2.2112 

2.3494 

2.4876 

2.6259 

20 

2.7640 

2.9022 

3.0404 

3.1786 

3.3168 

3.4552 

3.5933 

3.7315 

3.8696 

4.0078 

30 

4.1460 

4.2842 

4.4224 

4.5606 

4.6988 

4.8370 

4.9751 

5.1134 

5.2517 

5.3897 

40 

5.5280 

5.6666 

5.8044 

5.9426 

6.0808 

6.2191 

6.3572 

6.4954 

6.6336 

6.7718 

50 

6.9100 

7.0482 

7.1864 

7.3246 

7.4628 

7.6010 

7.7393 

7.8775 

8.0155 

8.1538 

60 

8.2920 

8.4303 

8.5684 

8.7066 

8.8448 

8.9830 

9.1212 

9.2594 

9.3976 

9.5359 

70 

9.6740 

9.8122 

9.9504 

10.088 

10.227 

10.365 

10.503 

10.641 

10.779 

10.918 

80 

11.056 

11.194 

11.322 

11.570 

11.609 

11.747 

11.885 

12.023 

12.161 

12.300 

90 

12.438 

12.576 

12.714 

12.855 

12.991 

13.129 

13.267 

13.405 

13.544 

13.682 

100 

13.820 

13.958 

14.096 

14.235 

14.373 

14.511 

14.649 

14.787 

14.925 

14.064 

Kilogrammetres  into  Foot=pounds 

• 

Kgm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 

Ft.-lb. 

0.0000 
72.334 
144.67 
217.00 
289.34 
361.66 
434.00 
507.34 
578.68 
651.00 
723.34 

Ft.-lb. 

7.2334 
79.567 
151.90 
224.23 
296.57 
368.89 
441.23 
514.57 
585.91 
658.23 
730.57 

Ft. -lb. 

14.467 
87.101 
158.43 
231.77 
304.11 
376.43 
448.77 
522.11 
593.45 
665.77 
738.11 

Ft.-lb. 

21.700 
94.034 
166.37 
238  70 
311.04 
383.36 
455.70 
529.04 
599.38 
672.70 
745.04 

Ft. -lb. 

28.934 
101.27 
173.60 
245.93 
318.27 
390.59 
462.93 
536.27 
607.61 
679.93 
752.27 

Ft.-lb. 

36.166 
108.50 
180.84 
253.17 
325.50 
397.82 
470.17 
543.50 
614.85 
687.17 
759.51 

Ft.-lb. 

43.400 
115.74 
188.08 
260-41 
332.75 
405.07 
477.41 
550.75 
622.09 
694.41 
76675 

Ft.-lb. 

50.734 
123.07 
195.40 
267.73 
340.07 
412.39 
484.73 
558.07 
629.41 
701.73 
774.07 

Ft.-lb. 

57.868 
130.20 
202.54 
274.87 
347.21 
419.53 
491.87 
565.21 
636.55 
708.87 
781.21 

Ft. -lb. 

65.100 
137.43 
209.77 
282.10 
354.44 
426.76 
499.10 
572.44 
643.78 
716.10 
788.44 

TlIK     MKTKIC    SYSTKM. 


507 


Conversion  of  Foot-tons  Into  Tonnes-metres. 


Foot-tons. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

0 

0.0000 

0.3097 

0.6194 

0.9291 

1.5484 

1.8581 

2.1678 

2. 177.") 

2.7-72 

10 

3.0969 

3.3166 

3.7163 

4.0260 

4.3356 

4.6453 

1.9550 

5.2667 

5.5744 

5  -11 

20 

6.1938 

6.4135 

6.8132 

7.1229 

7.4325 

7.7  U-J 

8.0519 

8.6713 

s.y.sio 

30 

9.2906 

9.6003 

9.9100 

10.219 

10.529 

L0.839 

11.149 

11.460 

1 1 .76> 

12.078 

40 

'       -■ 

L2.697 

13.006 

13.316 

13.626 

. 

14.245 

14.557 

14.864 

15.174 

50 

15.484 

15.791 

16.103 

16.413 

16.723 

17.342 

17.654 

17.961 

18.271 

60 

18.581 

19.200 

19.510 

19.820 

20.129 

20.439 

20.751 

21.058 

21.368 

70 

21.678 

21.988 

■j  j.  ■_".': 

22  6H7 

22.917 

23.226 

2  S.536 

23.848 

24  155 

24.466 

80 

24.775 

25.085 

_ 

25.704 

26.014 

26.323 

26.633 

26.945 

27.252 

27.562 

90 

27.872 

28  182 

28  v\ 

28.801 

29.111 

29.420 

29.730 

30.042 

30.349 

30.659 

100 

30.969 

31.279 

31.898 

32.208 

32.517 

33.139 

33.446 

33.756 

Conversion  of  Tonnes 

-metr 

es  into  Foot-tons 

• 

T. -metres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

F.-tu. 

l".-tn. 

F.-tu. 

F.-tu. 

F.-tu. 

F.-tu. 

F.-tn. 

F.-tn. 

F.-tu. 

F.-tn. 

0 

0.0000 

3.2290 

6.4581 

9.6871 

12.916 

16.1 15 

19.374 

22.603 

25.832 

29.061 

10 

32.290 

35.519 

:>.  TV 

41.977 

45.206 

48.435 

51.664 

54.893 

58.122 

61.351 

20 

64.581 

67.810 

71.049 

74.268 

77.497 

80.726 

83.955 

87.184 

90.413 

93.642 

30 

96.871 

100.10 

103.34 

106.56 

109.79 

113.01 

116.24 

119.47 

122.70 

125.98 

40 

129.16 

133.39 

l:;:...;:; 

138.85 

142.07 

1 15.30 

11-.:.:: 

151.76 

154.99 

158.22 

50 

161.15 

164.68 

167.92 

171.11 

174.36 

177.5m 

180.82 

184.05 

1*7.28 

190.51 

60 

193.74 

196.97 

200.21 

203.43 

206.65 

209.88 

213.11 

216  31 

219.57 

222.80 

70 

226.03 

229.26 

232.50 

235.72 

238.94 

242.17 

245.40 

248.63 

251.86 

255  39 

80 

'258.32 

261.55  264.79 

268.01 

271.23 

274.46 

277.69 

280.92 

284.15 

287.38 

90 

290.61 

293.84  297.08 

300.30 

303.52 

306.75 

309.98 

313.21 

316.44 

319.67 

100 

322.90 

326.13  329.37 

332.59 

335.81 

339.04 

342.27 

345.50 

348.73 

351.96 

British  Thermal  Units  into  Fren 

ch  Calories. 

B.  T.  U. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cai. 

Cal. 

0 

0.0000 

0.2520 

0.5040 

0.7560 

1.0080 

1.2600 

1.5120 

1.7640 

2.0160 

2.26«0 

10 

2  5200 

2.7720 

3.0240 

3.27m  i 

3.5280 

3.7800 

4.0320 

4.2-)'* 

4.5360 

4.7880 

20 

5.0399 

5.2919 

5-5439 

5.7959 

6.0478 

6.2699 

6.5419 

1    -       • 

7.0559 

7.3079 

30 

7.5600 

7.8120 

8.0640 

8.3160 

\5»Wi. 

8.8200 

9.0720 

9.3340 

9.5760 

y.v>o 

40 

10.080 

10.332 

10.584 

10.836 

11. OSS 

11.340 

11.512 

11.844 

12.096 

12.348 

50 

12.600 

13.104 

13.356 

13.608 

13.860 

14.112 

14.364 

14.616 

14.868 

60 

15  120 

15.372 

15.624 

15.876 

16.128 

16.38  1 

16.632 

16.884 

17.136 

17.388 

70 

17.640 

17.892 

is. Ill 

18.396 

1-. CIS 

18.900 

19.152 

19  404 

19.656 

19  908 

80 

20.160 

20.412 

20.664 

20.916 

21.168 

21.420 

21.672 

21.924 

22.176 

22.428 

90 

22.680 

22.932 

23.184 

23.436 

23.688 

23.940 

24.192 

24.444 

24.696 

24.948 

100 

25.200 

25.452  25.704 

25.956, 

26.208 

26.460 

26.712 

26.964 

27  216 

27.468 

French  Calories 

into  British  Thermal 

Units. 

Crtlories. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

T.  U. 

T.  U. 

T.  D. 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

T   D. 

T  U. 

T.  U. 

0 

0.0000 

3.9683 

7.9366 

11.905  1 

r.i.su 

23.810 

27.77s 

31.746 

35.715 

10 

39.683 

43.651 

47.620 

51.598  55.520 

59.525 

63.493 

67.401 

71.429 

75.398 

20 

79.366 

83.334 

91.271  95.203 

99.208 

103.17 

107.14 

111.11 

115  -38 

30 

119.05 

123.02 

126.98 

130.95  134.89 

138.89 

1 12  86 

146.83 

150.80 

154.77 

40 

158.73 

L62.70 

166.66 

170.62  174.57 

178.57 

186.51 

190.48 

!  M  15 

50 

198.42 

■2>>\1.  :'.• 

206.35 

210.39  214.26 

218.26 

222.23 

226.20 

230.16 

234.14 

60 

238  10 

242.07 

246.03 

.00 

253.94 

258.94 

261.91 

265.88 

269.85 

273.82 

70 

277  7s 

281.75 

285.72 

. 

297.62 

301.59 

305.56 

309.63 

313.50 

80 

317.46 

321.43 

325  10 

■ 

:  30  341.27 

345.24 

349.20 

353.18 

90 

857.15 

361.12 

365.09, 

369.05 

372.98 

376.99  380.96 

384.'.' 

392.87 

100 

396.83 

400.80 

404.77 

i    -  7 

412.67 

416.67 

420.64 

124  61 

132.66 

508 


Natural  Trigonometrical  Functions. 


I 


6 
p 

Pi 

ft 

M 

Sine. 

Vers. 
Cos. 

1.0000 

Cose- 
cant. 

Tang. 

Co- 

TANG. 

Inlin. 

Se- 
cant. 

Vers. 
Sin. 

Co- 
sine. 

to 

H 

6 

P 

~T 

0 

.00000 

Intin. 

.00000 

1.0000 

.00000 

1.0000 

10 

.00291 

.99709 

343.77 

.00291 

343.77 

1.0000 

.00000 

.99999 

50 

90 

20 

.00582 

.99418 

171.89 

.00582 

171.88 

1.0000 

.00002 

.99998 

40 

30 

.00873 

.99127 

114.59 

.00873 

114.59 

1.0000 

.00004 

.99996 

30 

40 

.011G3 

.98836 

85.946 

.01164 

85.940 

1.0001 

.00007 

.99993 

20 

50 

.01454 

.98546 

68.757 

.01454 

68.750 

1.0001 

.00010 

.99989 

10 

1 

0 

.01745 

.98255 

57.299 

.01745 

57.290 

1.0001 

.00015 

.99985 

89 

10 

.02036 

.97964 

49.114 

.02036 

49.104 

1.0002 

.00021 

.99979 

50 

20 

.02327 

.97673 

42.976 

.02327 

42.964 

1.0003 

.00027 

.99973 

40 

30 

.02618 

.97382 

38.201 

.02618 

38.188 

1.0003 

.00034 

.99966 

30 

40 

.02908 

.97091 

34.38J 

.02910 

34.368 

1.0004 

.00042 

.99958 

20 

50 

.03199 

.96801 

31.257 

.03201 

31.241 

1.0005 

.00051 

.99949 

10 

2 

0 

.03490 

.96510 

28.654 

.03492 

28.636 

1.0006 

.00061 

.99939 

88 

10 

.03781 

.96219 

26.450 

.03783 

26.432 

1.0007 

.00071 

.99928 

50 

20 

.04071 

.95929 

24.562 

.04075 

24.542 

1.0008 

.00083 

.99917 

40 

30 

.04362 

.95638 

22.925 

.04366 

22.904 

1.0009 

.00095 

.99905 

30 

40 

.04652 

.95347 

21.494 

.04657 

21.470 

1.0011 

.00108 

.99892 

20 

50 

.04943 

.95057 

20.230 

.04949 

20.205 

1.0012 

.00122 

.99878 

10 

3 

0 

.05234 

.94766 

19.107 

.05241 

19.081 

1.0014 

.00137 

.99863 

87 

10 

.05524 

.94476 

18.103 

.05532 

18.075 

1.0015 

.00153 

.99847 

50 

20 

.05814 

.94185 

17.198 

.05824 

17.169 

1.0017 

.00169 

.99831 

40 

30 

.06105 

.93895 

16.380 

.06116 

16.350 

1.0019 

.00186 

.99813 

30 

40 

.06395 

.93605 

15.637 

.06408 

15.605 

1.0020 

.00205 

.99795 

20 

50 

.06685 

.93314 

14.958 

.06700 

14.924 

1.0022 

.00224 

.99776 

10 

4 

0 

.06976 

.93024 

14.335 

.06993 

14.301 

1.0024 

.00243 

.99756 

86 

10 

.07266 

.92734 

13.763 

.07285 

13.727 

1.0026 

.00264 

.99736 

50 

20 

.07556 

.92444 

13.235 

.07577 

13.197 

1.0029 

.00286 

.99714 

40 

30 

.07846 

.92154 

12.745 

.07870 

12.706 

1.0031 

.00308 

.99692 

30 

40 

.08136 

.91864 

12.291 

.08163 

12.250 

1.0033 

.00331 

.99668 

20 

50 

.08426 

.91574 

11.868 

.08456 

11.826 

1.0036 

.00356 

.99644 

10 

5 

0 

.08715 

.91284 

11.474 

.08749 

11.430 

1.0038 

.00380 

.99619 

85 

10 

.09005 

.90995 

11104 

.09042 

11.059 

1.0041 

.00406 

.99594 

50 

20 

.09295 

.90705 

10.758 

.09335 

10.712 

1.0043 

.00433 

.99567 

40 

30 

.09584 

.90415 

10.433 

.09629 

10.385 

1.0046 

,00460 

.99540 

30 

40 

.09874 

.90126 

10.127 

.09922 

10.078 

1  0049 

.00489 

.99511 

20 

50 

.10163 

.89836 

9.8391 

.10216 

9.7882 

1.0052 

.00518 

.99482 

10 

6 

0 

.10453 

.89547 

9.5668 

.10510 

9.5144 

1.0055 

.00548 

.99452 

84 

10 

.10742 

.89258 

9.3092 

.10805 

9.2553 

1.0058 

.00579 

.99421 

50 

20 

.11031 

.88969 

9.0651 

.11099 

9.0098 

1.0061 

.00110 

.99390 

40 

30 

.11320 

.88680 

8.8337 

.11393 

8.7769 

1.0065 

.00643 

.99357 

30 

40 

.11609 

.88391 

8.6138 

.11688 

8.5555 

1.0068 

.00676 

.99324 

20 

50 

.11898 

.88102 

8.4046 

.11983 

8.3449 

1.0071 

.00710 

.99290 

10 

7 

0 

.12187 

.87813 

8.2055 

.12278 

8.1443 

1.0075 

.00745 

.99255 

88 

10 

.12476 

.87524 

8.0156 

.12574 

7.9530 

1.0079 

.00781 

.99219 

50 

20 

.12764 

.87236 

7.8344 

.12869 

7.7703 

1.0082 

.00818 

.99182 

40 

30 

.13053 

.86947 

7.6613 

.13165 

7.5957 

1.0086 

.00855 

.99144 

30 

40 

.13341 

.86659 

7.4957 

.13461 

7.4287 

1.0090 

.00894 

.99106 

20 

50 

.13629 

.86371 

7.3372 

.13757 

7.2687 

1.0094 

.00933 

.99067 

10 

8 

0 

.13917 

.86083 

7.1853 

.14054 

7.1154 

1.0098 

.00973 

.99027 

82 

10 

.14205 

.85795 

7.0396 

.14351 

6  9682 

1.0102 

.01014 

.98986 

50 

20 

.14493 

.85507 

6.8998 

.14648 

6.8269 

1.0107 

.01056 

.98944 

40 

30 

.14781 

.85219 

6.7655 

.14945 

6.6911 

1.0111 

.01098 

.98901 

30 

40 

.15068 

.84931 

6.6363 

.15243 

6.5605 

1.0115 

.01142 

.98858 

20 

50 

.15356 

.84644 

6.5121 

.15540 

6.4348 

1.0120 

.01186 

.98814 

10 

9 

0 

.15643 

.84356 

6.3924 

.15838 

6.3137 

1.0125 

.01231 

.98769 

81 

Co- 

Vers. 

Se- 

Co- 

Tan- 

Cose- 

Vers 

Sine. 

Sine. 

Sin. 

cant 

TANG. 

gent. 

cant. 

Cos. 

N  vtl'Ual  Trigonometrical  Function's. 


.VI!) 


— 

Sine. 

Vers. 
Cos. 

COSB- 

<  an  r. 

Ta>-g. 

Co- 

TAS(i. 

Sk- 

1    A  N    I  . 

V  i;ks. 

Sik. 

.01237 

c,,. 

BUTE. 

— 

- 

- 
- 

9 

.15043 

.84356 

6.3924 

.15838 

6.3137 

1.012.". 

28769 

81 

10 

.15031 

.84069 

6.2772 

.16137 

6.1970 

1.0129 

.01277 

.98723 

50 

20 

.16218 

.83782 

6.1661 

.16435 

6.0844 

1.0134 

.01324 

28676 

40 

30 

.1050') 

.83495 

6.0588 

.16734 

62758 

1.0139 

.01371 

28628 

30 

40 

.16791 

.83208 

52654 

.17033 

5.8708 

1  0144 

.01120 

28581 1 

20 

50 

.17078 

.82922 

5.8664 

.17333 

5.7694 

1.0149 

.01469 

.98531 

10 

10 

0 

.17365 

.82635 

5.7588 

.17633 

5.6713 

1.0154 

.01519 

.98481 

80 

10 

.17651 

.82349 

5.6653 

.17933 

5.5764 

1.0159 

21570 

.98430 

50 

20 

.17937 

.82062 

5.5749 

.18233 

5.4845 

1.0165 

.01622 

.9S37.S 

40 

30 

.18223 

.M776 

."..4874 

.18534 

5.39.V. 

1.0170 

.01674 

.98325 

30 

40 

.18509 

.81490 

5.4026 

.18835 

5.3093 

1.0176 

21728 

28272 

20 

50 

.18705 

.81205 

5.3205 

.19136 

5.2257 

1.0181 

.01782 

.98218 

10 

11 

0 

.l'.niM 

.80919 

.-.2408 

.19438 

5.1445 

1.0187 

.01837 

.98163 

79 

10 

.19366 

.8064 

5.1636 

.19710 

5.0658 

1.0193 

.01893 

.98107 

50 

20 

.19652 

.88348 

5.0886 

.20042 

42694 

1.0199 

21950 

.98050 

40 

30 

.19937 

.80063 

5.0158 

.20345 

4.9151 

1  .<  I2(  >:. 

.02007 

.9799.' 

30 

40 

■  >,  (•>•>•> 

.79778 

4. 94:. 2 

.20648 

4.8430 

1.0211 

.02066 

27934 

20 

50 

.20506 

.79493 

4.8765 

.20952 

4.7728 

1.0217 

.02125 

.97875 

10 

12 

0 

.20791 

.7'.»209 

4.8097 

.21256 

4.7046 

1.0223 

.02185 

.97815 

78 

10 

.21076 

.78924 

4.7448 

.21560 

4.6382 

1.0230 

.0-2246. 

.977.-4 

50 

20 

21360 

.7>'">40 

4.6817 

.21864 

4.5736,     1.0236 

.02308 

.97692 

40 

30 

.21044 

.78356 

4.6202 

.22169 

4. .-.107     10243 

22370 

.97630 

30 

40 

51928 

.78072 

4.5604 

.22475 

4.4494     1.0249 

.02434 

.97566 

20 

50 

.22211 

.77788 

4.5021 

22781 

4.3897 

1.0256 

.024;  is 

.97502 

10 

13 

0 

22495 

.77505 

4.4454 

.23087 

4.3315 

1.0263 

22563 

.97437 

77 

10 

.22778 

.77221 

4.3901 

.23393 

4.2747 

1.0270 

.02629 

.973,71 

50 

20 

23061 

.76938 

4.3362 

.2: '.700 

4.2193 

1.0277 

.02695 

40 

30 

.23344 

.76655 

4.2836 

.24008     4.1653 

1.0284 

.0276.. 

.97237 

30 

40 

.23627 

.76373 

42324 

.24316 

4.1127 

1.0291 

.02831 

.97169 

20 

60 

23910 

.76090 

4.1824 

.24624 

4.0611 

12299 

.02900 

.97099 

10 

14 

i) 

24192 

.75808 

4.1336 

.24933     4.01 

1.0306 

.02970 

27029 

76 

10 

.24474 

.75526 

4.0859 

25242     3.9616 

1.0314 

.03041 

50 

20 

.247.'.6 

.75244 

4.0394 

25552     3.9136 

1.0321 

.03113 

40 

30 

- 

.74962 

3.99  ■' 

25862    3.8667 

1.0329 

.03185 

.96815 

30 

40 

25319 

.74680 

3.9495 

.26172     3.8208 

1.0  87 

.031 

.96,74 1 

20 

50 

.25601 

.74399 

3.9061 

.26483  1  3.7759 

1.0345 

.03332 

.96667 

10 

15 

0 

25882 

.74118 

3.8637 

.26795  j  3.7320 

1.0.353 

.03407 

26592 

75 

10 

.261  13 

.73s  ;7 

3.8222 

.27107  |  3.6891 

1.0361 

.03483 

.96517 

50 

20 

26443 

.73556 

3.7816 

.27419     3.6470 

12369 

.03560 

.9(440 

40 

30 

.26724 

.73276 

3.7420 

.27732  1  3  6059 

1.0377 

.03637 

.96363 

30 

40 

.27004 

.72996 

.{.7031 

.28046  1  3.5656 

1.0386 

23716 

26285 

20 

:.o 

.27284 

.72716 

3.6651 

.28360 

3.5261 

1.0394 

.03794 

.96206 

10 

16 

0 

.27564 

.72436 

3.6279 

.28674 

3.487  \ 

1.0403 

.03874 

.96126 

74 

10 

.27843 

.72157 

3.5915 

.28990 

3.4495 

1.0412 

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.96045 

50 

20 

28122 

.71877 

3.5559 

.29305 

3.4124 

1.0420 

.04036 

40 

30 

.28401 

.71608 

3.5209 

.29621 

32759 

1.0429 

.04118 

25882 

30 

40 

.28680 

.71320 

3.4867 

.29938 

3.3402 

1.0438 

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.95799 

20 

50 

.28059 

.71041 

3.4532 

.30255 

3.3052 

1.0448 

24286 

.95715 

10 

17 

0 

.70763 

3.4203 

.30573 

3.2708 

1.0457 

.04369 

25630 

73 

10 

.29515 

.7048.-) 

3.3881 

.30891 

3.2371 

1.0466 

24455 

.95545 

50 

20 

.29793 

.70207 

3.3565 

,  .31210 

3.2041 

1.0476 

.04541 

.95459 

40 

36 

.30070 

.69929 

3.32V. 

.31530 

3.1716 

1.0485 

.01628 

.'.'.-.3,72 

30 

40 

.30348 

.69652 

3.2961 

.31850 

3.1397 

1.(495 

.(4716 

.95284 

20 

50 

.30625 

.69375 

3.2653 

.32171 

3.1064 

1.0505 

.04806 

25195 

10 

18 

0 

.30902 

.69098 



Vers. 

3.2361 

.32492 

3.0777 

1.0515 

.04894 

26106 



72 

Co- 

Se- 

CO- 

Tan- 

Cobb- 

Vi 

Sine. 

sine. 

Sin. 

cant. 

TANG. 

gent. 

(ANT. 

510 


Natural  Trigonometrical  Functions. 


P 

0 

Sine. 

Vers. 

Cos. 

Cose- 
cant. 

Tang. 

Co- 

TANG. 

Se- 
cant. 

Vers. 
Sin. 

Co- 
sine. 

0 
Q 

18 

.30902 

.69098 

3.2361 

.32492 

3.0777 

1.0515 

.04894 

.95106 

~T2 

10 

.31178 

.68822 

3.2074 

.32814 

3.0475 

1.0525 

.049S5 

.95015 

50 

20 

.31454 

.68545 

3.1792 

.33136 

3.0178 

1.0535 

.05076 

.94924 

40 

30 

.31730 

.68269 

3.1515 

.33459 

2.9887 

1.0545 

.05168 

.94832 

30 

40 

.32006 

.67994 

3.1244 

.33783 

2.9600 

1.0555 

.05260 

.94740 

20 

50 

.32282 

.67718 

3.0977 

.34108 

2.9319 

1.0566 

.05354 

.94646 

10 

19 

0 

.32557 

.67443 

3.0715 

.34433 

2.9042 

1.0576 

.05448 

.94552 

71 

10 

.32832 

.67168 

3.0458 

.34758 

2.8770 

1.0587 

.05543 

.94457 

50 

20 

.33106 

.66894 

3.0206 

.35085 

2.8502 

1.0598 

.05639 

.94361 

40 

30 

.33381 

.66619 

2.9957 

.35412 

2.8239 

1.0608 

.05736 

.94264 

30 

40 

.33655 

.66345 

2.9713 

.35739 

2.7980 

1.0619 

.05833 

.94167 

20 

50 

.33928 

.66071 

2.9474 

.36068 

2.7725 

1.0630 

.05932 

.94068 

10 

20 

0 

.34202 

.65798 

2.9238 

.36397 

2.7475 

1.0642 

.06031 

.93969 

70 

10 

.34475 

.65525 

2.9006 

.36727 

2.7228 

1.0653 

.06131 

.93869 

50 

20 

.34748 

.65252 

2.8778 

.37057 

2.6985 

1.0664 

.06231 

.93769 

40 

30 

.35021 

.64979 

2.8554 

.37388 

2.6746 

1.0676 

.06333 

.93667 

30 

40 

.35293 

.64707 

2.8334 

.37720 

2.6511 

1.0688 

.06435 

.93565 

20 

50 

.35565 

.64435 

2.8117 

.38053 

2.6279 

1.0699 

.06538 

.93462 

10 

21 

0 

.35837 

.64163 

2.7904 

.38386 

2.6051 

1.0711 

.06642 

.93358 

69 

10 

.3(5108 

.63892 

2.7694 

.38720 

2.5826 

1.0723 

.06747 

.93253 

50 

20 

.36379 

.63621 

2.7488 

.39055 

2.5605 

1.0736 

.00852 

.93148 

40 

30 

.36650 

.63350 

2.7285 

.39391 

2.5386 

1.0748 

.06958 

.93042 

30 

40 

.36921 

.63079 

2.7085 

.39727 

2.5171 

1.0760 

.07065 

.92935 

20 

50 

.37191 

.62809 

2.6888 

.40065 

2.4960 

1.0773 

.07173 

.92827 

10 

22 

0 

.37461 

.02539 

2.6695 

.40403 

2.4751 

1.0785 

.07282 

.92718 

68 

10 

.37730 

.62270 

2.6504 

.40741 

2.4545 

1.0798 

.07391 

.92609 

50 

20 

.37999 

.62000 

2.6316 

.41081 

2.4342 

1.0811 

.07501 

.92499 

40 

30 

.38268 

.61732 

2.6131 

.41421 

24142 

1.0824 

.07612 

.92388 

30 

40 

.38537 

.61463 

2.5949 

.41762 

2.3945 

1.0837 

.07724 

.92276 

20 

50 

•38805 

.61195 

2.5770 

.42105 

2.3750 

1.0850 

.07836 

.92164 

10 

23 

0 

.39073 

.60927 

2.5593 

.42447 

2.3558 

1.0S64 

.07949 

.92050 

67 

10 

.39341 

.60659 

2.5419 

.42791 

2.3369 

1.0877 

.08063 

.91936 

50 

20 

.39608 

.60392 

2.5247 

.43136 

2.3183 

1.0891 

.08178 

.91822 

40 

30 

.39875 

.60125 

2.5078 

.43481 

2.2998 

1.0904 

.08294 

.91706 

30 

40 

.40141 

.59858 

2.4912 

.43827 

2.2817 

1.0918 

.08410 

.91590 

20 

50 

.40408 

.59592 

2.4748 

.44175 

2.2637 

1.0932 

.08527 

.91472 

10 

24 

0 

.40674 

.59326 

2.4586 

.44523 

2.2460 

1.0946 

.08645 

.91354 

66 

10 

.40939 

.59061 

2.4426 

.44872 

2.2286 

1.0961 

.08764 

.91250 

50 

20 

.41204 

.58795 

2.4269 

.45222 

2.2113 

1.0975 

.08884 

.91116 

40 

30 

.41469 

.58531 

2.4114 

.45573 

2.1943 

1.0989 

.09004 

.90996 

30 

40 

.41734 

.58266 

2.3961 

.45924 

2.1775 

1.1004 

.09125 

.90S75 

20 

50 

.41998 

.58002 

2.3811 

.46277 

2.1609 

1.1019 

.09247 

.90753 

10 

25 

0 

.42262 

.57738 

2.3662 

.46631 

2.1445 

1.1034 

.09369 

.90631 

65 

10 

.42525 

.57475 

2.3515 

.46985 

2.1283 

1.1049 

.09492 

.90507 

50 

20 

.42788 

.57212 

2.3371 

.47341 

2.1123 

1.1064 

.09617 

.90383 

40 

30 

.43051 

.56949 

2.3228 

.47697 

2.0965 

1.1079 

.09741 

.90258 

30 

40 

.43313 

.56686 

2.3087 

.48055 

2.0809 

1.1095 

.09867 

.90133 

20 

50 

.43575 

•56424 

2.2949 

.48414 

2.0655 

1.1110 

.09993 

.90006 

10 

26 

0 

.43837 

.56163 

2.2812 

.48773 

2.0503 

1.1126 

.10121 

.89879 

64 

10 

.44098 

.55902 

2.2676 

.49134 

2.0352 

1.1142 

.10248 

.89751 

50 

20 

.44359 

.55641 

2.2543 

.49495 

2.0204 

1.1158 

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.89623 

40 

30 

.44620 

.55380 

2.2411 

.49858 

2.0057 

1.1174 

.10506 

.89493 

30 

40 

.44880 

.55120 

2.2282 

.50222 

1.9912 

1.1190 

.10637 

.89363 

20 

50 

.45140 

.54860 

2.2153 

.50587 

1.9768 

1.1207 

.10768 

.89232 

10 

27 

.45399 

.54601 

2.2027 

.50952 

1.9626 

1.1223 

.10899 

.89101 
Sine. 

63 

Co- 

Vers. 

Se- 

Co- 

Tan. 

Cose- 

Vers. 

sine. 

Sin. 

cant. 

tang.  GENT. 

cant. 

Cos. 

Natural  Trigonometrical  Functions 

:.ll 

C5 

— 

9 
0 

Sim:. 

\  ER8. 
1  OS. 

i  '  (SE- 
CANT. 

Tang. 

Co. 

TANG. 

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Sin. 

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— 
— 

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27" 

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2.2027 

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1.9626 

1.1223 

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2.1902 

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1.9486 

1.1240 

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.88968 

50 

20 

.45917 

.54083 

2.1778 

.51687 

L.9347 

1.1257 

.11165 

.88835 

10 

30 

.46175 

.53825 

2.1657 

.52057 

1.9210 

1.1274 

.11299 

.88701 

30 

40 

.4  S433 

.53567 

2.1536 

.52427 

1.9074 

1.1291 

.11434 

66 

20 

66 

.46690 

.53310 

2.1418 

.52798 

1.8940 

1.1308 

.11569 

.88431 

10 

28 

0 

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2.1300 

£3171 

1.8807 

1.1326 

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.88295 

62 

10 

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2.  n.s.-. 

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1.8676 

1.1343 

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.88158 

50 

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2.1070 

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1.8546 

1.1361 

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10 

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2.0957 

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1.8418 

1.1579 

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30 

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2.0846 

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1.8291 

1.1397 

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20 

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1.8165 

1.1415 

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1.8040 

1.1433 

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1.7917 

1.1452 

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50 

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2.0413 

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1.7795 

1.1471 

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40 

30 

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2.0308 

£6577 

1.7675 

1.1489 

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30 

40 

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£0505 

2.0204 

£6962 

1.7555 

1.1508 

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.86892 

20 

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2.0101 

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1.7437 

1.1528 

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10 

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1.7320 

1.1547 

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1.9900 

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1.9801 

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1.1586 

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1.9703 

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1.6977 

1.1606 

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1.9606 

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1.6864 

1.1626 

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20 

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1.9510 

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1.6753 

1.1646 

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10 

31 

0 

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1.9416 

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1.6643 

1.1666 

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.85717 

59 

10 

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.48247 

1.9322 

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1.6534 

1.1687 

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1.9230 

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1.6425 

1.1707 

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40 

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£2250 

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1.9139 

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1.6318 

1.1728 

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1.6212 

1.1749 

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1.8959 

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1.6107 

1.1770 

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32 

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1.6003 

1.1792 

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58 

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1.8783 

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1.5900 

1.1813 

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1.8697 

1.5798 

1.1835 

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40 

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53730 

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1.8611 

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1.5697 

1.1857 

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30 

40 

"     75 

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1.8527 

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1.5596 

1.1879 

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1.8443 

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1.5497 

1.1901 

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10 

33 

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1.8361 

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1£399 

1.1924 

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57 

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1.8279 

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1.5301 

1.1946 

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1.4826 

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1.4733 

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56401 

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1.4460 

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1.7434 

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1.4106 

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1.3848 

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54 

Co- 

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cant 

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-2_  0-<=  *- 

Natural   Trigonometrical   Functions. 


6 

W 
A 

ft 

M 

0 

Sine. 

Vers. 
Cos. 

Cose- 
cant. 

Tang. 

Co- 

TANG. 

Se- 
cant. 

Vers. 

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Co- 
sine. 

to 

6 
A 

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.41221 

1.7013 

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1.3764 

1.2361 

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54" 

10 

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1.6945 

.73100 

1.3680 

1.2387 

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50 

20 

59248 

.40752 

1.6878 

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1.3597 

1.2413 

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.80558 

40 

30 

.59482 

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1.6812 

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1.3514 

1.2440 

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.80386 

30 

40 

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.40284 

1.6746 

.74447 

1.3432 

1.2407 

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.80212 

20 

50 

.59949 

.40051 

1.6681 

.74900 

1.3351 

1.2494 

.19962 

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10 

37 

0 

.60181 

.39818 

1.6616 

.75355 

1.3270 

1.2521 

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53 

10 

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.39586 

1.6552 

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1.3190 

1.2549 

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.79688 

50 

20 

.60645 

.39355 

1.6489 

.76271 

1.3111 

1.2577 

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.79512 

40 

30 

.60876 

.39124 

1.6427 

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1.3032 

1.2605 

.20665 

.79335 

30 

40 

.61107 

.38893 

1.6365 

.77196 

1.2954 

1.2033 

.20842 

.79158 

20 

50 

.61337 

.38663 

1.6303 

.77661 

1.2876 

1.2661 

.21020 

.78980 

10 

38 

0 

.61566 

.38434 

1.6243 

.78128 

1.2799 

1.2690 

.21199 

.78801 

52 

10 

.61795 

.38205 

1.6182 

.78598 

1.2723 

1.2719 

.21378 

.78622 

50 

20 

.62023 

.37976 

1.6123 

.79070 

1.2647 

1.2748 

.21558 

.78441 

40 

30 

.62251 

.37748 

1.6064 

.79543 

1.2572 

1.2778 

.21739 

.78261 

30 

40 

.62479 

.37521 

1.6005 

.80020 

1.2497 

1.2S07 

.21921 

.78079 

20 

50 

.62706 

.37294 

1.5947 

.80498 

1.2423 

1.2837 

.22103 

.77897 

10 

39 

0 

.62932 

.37068 

1.5890 

.80978 

1.2349 

1.2867 

.222S5 

.77715 

51 

10 

.63158 

.36842 

1.5833 

.81461 

1.2276 

1.2898 

.22469 

.77531 

50 

20 

.63383 

.36617 

1.5777 

.81946 

1.2203 

1.2929 

.22653 

.77347 

40 

30 

.63608 

.36392 

1.5721 

.82434 

1.2131 

1.2960 

.22837 

.77102 

30 

40 

.63832 

.36168 

1.5666 

.82923 

1.2059 

1.2991 

.23023 

.76977 

20 

50 

.64056 

.35944 

1.5611 

.83415 

1.1988 

1.3022 

.23209 

.76791 

10 

40 

0 

.64279 

.35721 

1.5557 

.83910 

1.1917 

1.3054 

.23395 

.76604 

50 

10 

.64501 

.35499 

1.5C,03 

.84407 

1.1847 

1.3086 

.23583 

.76417 

50 

20 

.64723 

.35277 

1.5450 

.84906 

1.1778 

1.3118 

.23771 

.76229 

40 

30 

.64945 

.35055 

1.5398 

.8540S 

1.1708 

1.3151 

.23959 

.76041 

30 

40 

.65166 

.34834 

1 .5345 

.85912 

1.1640 

1.3184 

.24149 

.75851 

20 

50 

.65386 

.34614 

1.5294 

.86419 

1.1571 

1.3217 

.24338 

.75661 

10 

41 

0 

.65606 

.34394 

1.5242 

.86929 

1.1504 

1.3250 

.24529 

.75471 

49 

10 

.65825 

.34175 

1.5192 

.87441 

1.1436 

1.3284 

.24720 

.75280 

50 

20 

.66044 

.33956 

1.5141 

.87955 

1.1369 

1.3318 

.24912 

.75088 

40 

30 

.66262 

.33738 

1.5092 

.88472 

1.1303 

1.3352 

.25104 

.74895 

30 

40 

.66479 

.33520 

1.5042 

.88992 

1.1237 

1.3386 

.25297 

.74702 

20 

50 

.66697 

.33303 

1.4993 

.89515 

1.1171 

1.3421 

.25491 

.74509 

10 

42 

0 

.66913 

.33087 

1.4945 

.90040 

1.1106 

1.3456 

.25685 

.74314 

48 

10 

.67129 

.32871 

1.4897 

.90568 

1.1041 

1.3492 

.25880 

.74119 

50 

20 

.67344 

.32656 

1.4849 

.91099 

1.0977 

1.3527 

.26076 

.73924 

40 

30 

.67559 

.32441 

1.4802 

.91633 

1.0913 

1.3563 

.26272 

.73728 

30 

40 

.67773 

.32227 

1.4755 

.92170 

1.0849 

1.3600 

.26469 

.73531 

20 

50 

.67987 

.32013 

1.4709 

.92709 

1.0786 

1.3636 

.26666 

.73333 

10 

43 

0 

.68200 

.31800 

1.4663 

.93251 

1.0724 

1.3673 

.26865 

.73135 

47 

10 

.68412 

.31588 

1.4617 

.93797 

1.0661 

1.3710 

.27063 

.72937 

50 

20 

.68624 

.31376 

1.4572 

.94345 

1.0599 

1.3748 

.27263 

.72737 

40 

30 

.68835 

.31164 

1.4527 

.94896 

1.0538 

1.3786 

.27462 

.72537 

30 

40 

.69046 

.30954 

1.4483 

.95451 

1.0476 

1.3824 

.27663 

.72337 

20 

50 

.69256 

.30744 

1.4439 

.96008 

1.0416 

1.3863 

.27864 

.72136 

10 

44 

0 

.69466 

.30534 

1.4395 

.96569 

1.0355 

1.3902 

.28066 

.71934 

46 

10 

.69675 

.30325 

1.4352 

.97133 

1.0295 

1.3941 

.28268 

.71732 

50 

20 

.69883 

.30117 

1.4310 

.97699 

1.0235 

1.3980 

.28471 

.71529 

40 

30 

.70091 

.29909 

1.4267 

.98270 

1.0176 

1.4020 

.28675 

.71325 

30 

40 

.70298 

.29702 

1.4225 

.98843 

1.0117 

1.4060 

,28879 

.71121 

20 

50 

.70505 

.29495 

1.4183 

.99420 

1.0058 

1.4101 

.29084 

.70916 

10 

45 

0 

.70711 

.29289 
Vers. 

1.4142 

Se- 

1 0000 

1.0000 
Tan- 

1.4142 

.29289 
Vers. 

.70711 

45 

Co- 

Co- 

Cose- 

Sine. 

sine. 

Sin. 

cant. 

TANG. 

gent. 

cant. 

Cos. 

CIRCUMFERENCE    AND    AREA    OF    CIRCLES. 


The  Circle. 


Notation. 


d  =  diameter  of  the  circle. 
r  =  radius  of  the  circle. 
p  =  periphery  or  circumference. 
a  —  area  of  a  circle  or  part  th< 
6  —  length  of  a  circle-arc. 


c  =  chord  of  a  segment,  length  of. 

h       height  of  a  segment. 

8  —  side  of  a  regular  polygon. 

v  =  centre  angle. 
w  =  polyLr"i!  angle. 


All  measures  must  be  expressed  in  terms  of  the  same  unit. 


Formulas  for  the  Circle. 


]'>  riplu  rij  or  ( 'ircitinf'  r- 
'  nee. 

nd        --=  3.14J. 
p       2wt  6.28r. 

p  =  2>/7ru  =  3.541  a. 
2a  An 

p  -  —  =  -d  • 


IHartu  U  r 

(<//'/  Radius. 

d  ■  =  -P- 

TT 

P 

3.11' 

P 

P 

'         2* 

6.28  ' 

d    =  2^ 

=  1.128V'a^ 

r~    V 

=  0.5011  <(. 

.!;>(£  f//  fftg  Circle. 


a^-77'/"       0.7854d* 
4 


a  nr- 


.14r2. 


a 


a 


Itt         12.56 " 
pd 

2  4    ' 


n  =  3.141  592  653  589  793  238  1621         33  279  502  884  197  169  399 


185 

Zn  =    9.424  778 

12.566  370 

5tt  =  15.707 

Itt         21.991    148 

25.132741 

9tt 


\tt  =  0.785  398 
\-  =  1.047  197 
%v  1.570  796 
1  .n  =  0.392  699 
',,-  0.523  599 
x\n  0.261  799 
-..-       2.094  394 

0.008 


Log.  -       0.497  149  372  69413 
513 


1 

TT 

=  0.318  310 

360 

.    TT 

114.5915 

■J 
77 

0.636  619 

Tr2  = 

9.869  650 

3 

7T 

0.954  929 

,rr 

1.772  453 

1 
TT 

f. 
7T 

8 

TT 

1.273  2 

4- 

0.564  1»9 

1.909  859 

v. 

1.253  314 

2.546  478 

12 

TT 

319  718 

si 

0.797  --1 

514 

Circumference  and   Area   of   Circles. 

Cirrum. 

Area. 

Circuru. 

Area. 

Circnna. 

Area. 

Diam- 

/^~V 

/^H^. 

Diam- 

/-~X 

i^HS. 

;Diam- 

y^~>\ 

^H?\ 

eter. 

o 

fp 

eter. 
51 

o 

fP 

1  eter. 
101 

o 

fP 

1 

3.1416 

0.7854 

160.22 

1 
2042.8 

317.30 

8011.9 

2 

6.2832 

3.1416 

52 

163.36 

2123.7 

102 

320.44 

8171.3 

3 

9.4248 

7.06S6 

53 

166.50 

2206.2  v 

103 

323.58 

8332.3 

4 

12.566 

12.5664 

54 

169.65 

2290.2 

104 

326.73 

8494.9 

5 

15.708 

19.6350 

55 

172.79 

21 575.8 

105 

329.87 

8659.0 

6 

18.850 

28.2743 

56 

175.93 

2463.0 

106 

333.01 

8824.7 

7 

21.991 

38.4845 

57 

179.07 

2551.8 

107 

336.15 

■  8992.0 

8 

25.133 

50.2655 

58 

182.21 

2642.1 

108 

339.29 

9160.9 

9 

28.274 

63.6173 

59 

185.35 

2734.0 

109 

342.43 

9331.3 

10 

31.416 

78.54 

60 

188.50 

2827.4 

110 

345.58 

9503.3 

11 

34.558 

95.03 

61 

191.64 

2922.5 

111 

348.72 

9676.9 

12 

37.699 

113.10 

62 

194.78 

3019.1 

112 

351.86 

9852.0 

13 

40.841 

132.73 

63 

197.92 

3117.2 

113 

355.00 

10028.8 

14 

43.982 

153.94 

64 

201.06 

3217.0 

114 

358.14 

10207.0 

15 

47.124 

176.71 

65 

204.20 

3318.3 

115 

361.28 

10386.9 

10 

50.265 

201.06 

66 

207.35 

3421.2 

116 

364.42 

10568.3 

17 

53.407 

226.98 

67 

210.49 

3525.7 

117 

367.57 

10751.3 

18 

56.549 

254.47 

68 

213.63 

3631.7 

118 

370.71 

10935.9 

19 

59.690 

283.53 

69 

216.77 

3739.3 

119 

373.85 

11122.0 

20 

62.832 

314.16 

70. 

219.91 

3848.5 

120 

376.99 

11310 

21 

65.973 

346.36 

71 

223.05 

3959.2 

121 

380.13 

11499 

22 

69.115 

380.13 

72 

226.19 

4071.5 

122 

383.27 

11690 

23 

72.257 

415.48 

73 

229.34 

418.-).  4 

123 

386.42 

11882 

24 

75.398 

452.39 

74 

232.48 

4300.8 

124 

389.56 

12076 

25 

78.540 

490.87 

75 

235.62 

4417.9 

125 

392.70 

12272 

26 

81.681 

530.93 

76 

238.76 

4536.5 

126 

395.84 

12469 

27 

84.823 

572.56 

77 

241.90 

4656.6 

127 

398.98 

12668 

28 

87.965 

615.75 

78 

245.04 

4778.4 

128 

402.12 

12868 

29 

91.106 

660.52 

79 

248.19 

4901.7 

129 

405.27 

1  1307P 

30 

94.248 

706.86 

80 

251.33 

5026.6 

130 

408.41 

13273 

31 

97.389 

754.77 

81 

254.47 

5153.0 

131 

411.55 

13478 

32 

100.53 

804.25 

82 

257.61 

5281.0 

132 

414.69 

13685 

33 

103.67 

855.30 

83 

260.75 

5410.6 

133 

417.83 

13893 

34 

106.81 

907.92 

84 

263.89 

5541.8 

134 

420.97 

14103 

35 

109.96 

962.11 

85 

267.04 

5674.5 

135 

424.12 

14314 

36 

113.10 

1017.88 

86 

270.18 

5808.8 

136 

427.26 

14527 

37 

116.24 

1075.21 

87 

273.32 

5944.7 

137 

430.40 

14741 

38 

119.38 

1134.11 

88 

276.46 

6082.1 

138 

433.54 

14957 

39 

122.52 

1194.59 

89 

279.60 

6221.1 

139 

436.68 

15175 

40 

125.66 

1256.63 

90 

282.74 

6361.7 

140 

439.82 

15394 

41 

128.81 

1320.25 

91 

285.SS 

C503.9 

141 

442.96 

15615 

42 

131.95 

1385.44 

92 

289.03 

6647.6 

142 

446.11 

15837 

43 

135.09 

1452.20 

93 

292.17 

6792.9 

143 

449.25 

16061 

44 

138.23 

1520.52 

94 

295.31 

6939.8 

144 

452.39 

16286 

45 

141.37 

1590.43 

95 

298.45 

7088.2 

145 

455.53 

16513 

46 

144.51 

1661.90 

96 

301.59 

7238.2 

146 

458.67 

16742 

47 

147.65 

1734.94 

97 

304.73 

7389.8 

147 

461.81 

16972 

48 

150.80 

1809.55 

98 

307.88 

7543.0 

148 

464.96 

17203 

49 

153.94 

1885.74 

99 

311.02 

7697.7 

149 

468.10 

17437 

50 

157.08 

1963.50 

100 

314.16 

7854.0 

150 

471.24 

17671 

Circumference   and   Abba    of   Circles. 


-  >  i  -j 


1  Circum. 

Area. 

Circum. 

An  a. 

Circum. 

Area. 

Diam- 

•""V 

>g||?s 

Diam- 

S~~\ 

^§H>- 

Diam- 

/"">. 

/-~^\ 

eter. 

iO 

474.38 

w 

eter. 
201 

o 

31731 

•  ter. 
251 

o 

o 

151 

17908 

631.  If, 

788.54 

49481 

15-2 

477.52 

18146 

202 

634.60 

32047 

252 

:  '1.68 

49876 

158 

1   480.66 

18 

203 

637.74 

:  12365 

794.82 

5027:', 

154 

483.81 

18627 

204 

640.S9 

321 

254 

797.96 

50671 

155 

486.95 

18869 

2i  15 

644.03 

:::;o06 

255 

801.11 

-1071 

156 

490.09 

19113 

206 

647.17 

:29 

256 

mi  1.25 

51 172 

157 

493.23 

1  '159 

207 

650.31 

33654 

257 

807.39 

51875 

158 

4%.37 

19607 

■_>,  IS 

65:'..  (5 

33979 

258 

810."  '• 

62279 

159 

499.51 

19856 

209 

656.59 

34307 

259 

813.67 

52685 

160 

502.65 

20106 

210 

659.73 

34636 

260 

816.81 

53093 

161 

505.80 

20358 

211 

662.88 

34967 

261 

819.96 

53502 

162 

50S.94 

20612 

212 

666.02 

35299 

262 

823.10 

"..'.913 

163 

512.08 

20867 

213 

669.16 

35633 

. 

826.24 

54325 

164 

515.22 

21121 

214 

672.30 

35968 

264 

829.38 

54739 

165 

518.36 

21382 

215 

675.41 

36305 

265 

832.:.  2 

55155 

166 

521.50 

21642 

216 

678.58 

36641 

266 

835.66 

55572 

167 

524.65 

J1904 

217 

681.7:'. 

36984 

267 

838.81 

.".5990 

16& 

527.79 

22167 

218 

684.87 

37325 

268 

841.95 

56410 

169 

530.93 

22432 

219 

688.01 

37668 

269 

8 15.09 

56832 

170 

534.07 

22698 

220 

691.15 

38013 

270 

848.2:: 

.",7256 

171 

537.21 

22966 

221 

694.29 

38360 

271 

851.37 

r>7680 

172 

540.35 

21 1235 

222 

697.43 

38708 

272 

854.51 

58107 

173 

543.50 

23506 

223 

700.58 

39057 

273 

857.66 

58535 

174 

546.64 

23779 

224 

703.72 

39408 

274 

860.80 

58965 

175 

549.78 

24053 

225 

706.86 

39761 

275 

863.94 

59396 

176 

552.92 

24328 

226 

710.00 

40115 

276 

S67.08 

59828 

177 

556.06 

24606 

227 

713.14 

40471 

277 

870.22 

60263 

178 

559.20 

24885 

228 

716.28 

40828 

278 

873.36 

60699 

179 

562.35 

25165 

229 

719.42 

41187 

279 

876.50 

61136 

180 

565.49 

254  17 

230 

722.57 

41548 

280 

879.65 

61575 

181 

568.63 

25730 

231 

725.71 

41910 

281 

882.79 

62016 

182 

571.77 

26016 

728.85 

42273 

282 

885.93 

•  ■.215S 

lv, 

574.91 

26302 

233 

731.99 

42638 

2S3 

889.07 

62902 

184 

578.05 

26590 

234 

735.13 

43005 

2S4 

892.21 

63347 

185 

581.19 

26880 

2 

738.27 

43374 

285 

895.35 

'•.'.794 

186 

584.::  1 

27172 

236 

711.42 

43744 

286 

898.50 

64242 

187 

587.48 

"165 

237 

744.56 

44115 

287 

901.64 

64692 

lv? 

590.62 

27759 

238 

717.70 

44488 

2^ 

901.7s 

65114 

189 

59: 

28055 

239 

750.84 

11863 

289 

907.92 

65597 

190 

596.90 

:53 

240 

:.98 

45239 

290 

911.06 

66052 

191 

600.U4 

28652 

241 

757.12 

45617 

291 

914.20 

66508 

192 

603.19 

29255 

212 

|.27 

15996 

292 

917.35 

66966 

193 

606.33 

.11 

46377 

920.49 

6712.) 

194 

.609.47 

29! 

244 

766 

46759 

923.63 

67887 

195 

612.61 

245 

•  69 

17114 

295 

926.77 

68349 

196 

615.75 

L72 

246 

772.83 

17529 

1.91 

68813 

197 

618.89 

30481 

217 

77" 

47916 

I  05 

69279 

1- 

2.04 

30791 

248 

■12 

.19 

717 

199 

.18 

::i: 

299 

939.34 

7021.". 

200 

628.32 

31416 

250   1 

7.85.40 

49087 

300 

942  18 

70- 

516 


Circumference   and   Area   of   Circles. 


Circuin 

Area. 

Circum 

Area. 

Circum 

Area. 

Diam- 

/"~\ 

i^m^. 

Diam- 

/■> 

^^. 

Diam- 

•"""V 

.gss*. 

eter. 

o 

IP 

eter. 
351 

o 

^ 

eter. 

o 

IP 

301 

945.62 

71158 

1102.70 

96  762 

401 

1259.78 

126  293 

302 

948.76 

71631 

352 

1105.S4 

97  314 

402 

1262.92 

126  923 

303 

951.90 

72107 

353 

1108.98 

97  868 

403 

1266.06 

127  556 

304 

955.04 

72583 

354 

1112.12 

98  423 

404 

1269.20 

128  190 

305 

958.19 

73062 

355 

1115.27 

98  980 

405 

1272.35 

128  825 

306 

961.33 

73542 

356 

1118.41 

99  538 

'196 

1275.49 

129  462 

307 

964.47 

74023 

357 

1121.55 

100  098 

407 

1278.63 

130  100 

308 

967.61 

74506 

358 

1124.69 

100  660 

408 

1281.77 

130  741 

309 

970.75 

74991 

359 

1127.83 

101  223 

409 

1284.91 

131  382 

310 

973.89 

75477 

360 

1130.97 

101  788 

410 

1288.05 

132  025 

311 

977.04 

75964 

361 

1134.11 

102  354 

411 

1291.19 

132  670 

312 

980.18 

76454 

362 

1137.26 

102  922 

412 

1294.34 

133  317 

313 

983.32 

76945 

363 

1140.40 

103  491 

413 

1297.48 

133  965 

314 

986.46 

77437 

364 

1143.54 

104  062 

414 

1300.62 

134  614 

315 

989.60 

77931 

365 

1146.68 

104  635 

415 

1303.76 

135  265 

316 

992.74 

78427 

366 

1149.82 

105  209 

416 

1306.90 

135  918 

317 

995.88 

78924 

367 

1152.96 

105  785 

417 

1310.04 

136  572 

318 

999.03 

79423 

368 

1156.11 

106  362 

418 

1313.19 

137  228 

319 

1002.17 

79923 

369 

1159.25 

106  941 

419 

1316.33 

137  885 

320 

1005.31 

80425 

370 

1162.39 

107  521 

420 

1319.47 

138  544 

321 

1008.45 

80928 

371 

1165.53 

108  103 

421 

1322.61 

139  205 

322 

1011.59 

81433 

372 

1168.67 

108  687 

422 

1325.75 

139  867 

323 

1014.73 

81940 

373 

1171.81 

109  272 

423 

1328.89 

140  531 

324 

1017.88 

82448 

374 

1174.96 

109  858 

424 

1332.04 

141 196 

325 

1021.02 

82958 

375 

1178.10 

110  447 

425 

1335.18 

141  863 

326 

1024.16 

83469 

376 

1181.24 

111  036 

426 

1338.32 

142  531 

327 

1027.30 

83982 

377 

1184.38 

111628 

427 

1341.46 

143  201 

328 

1030.44 

84496 

378 

1187.52 

112  221 

428 

1344.60 

143  872 

329 

1033.58 

85012 

379 

1190.66 

112  815 

429 

1347.74 

144  545 

330 

1036.73 

85530 

380 

1193.81 

113  411 

430 

1350.88 

145  220 

331 

1039.87 

86049 

381 

1196.95 

114  009 

431 

1354.03 

145  896 

332 

1043.01 

86570 

382 

1200.09 

114  608 

432 

1357.17 

146  574 

333 

1046.15 

87092 

383 

1203.23 

115  209 

433 

1360.31 

147  254 

334 

1049.29 

87616 

384 

1206.37 

115  812 

434 

1363.45 

147  934 

335 

1052.43 

88141 

385 

1209.51 

116  416 

435 

1366.59 

148  617 

336 

1055.58 

88668 

386 

1212.65 

117  021 

436 

1369.73 

149  301 

337 

1058.72 

89197 

387 

1215.80 

117  628 

437 

1372.88 

149  987 

338 

1061.86 

89727 

388 

1218.94 

118  237 

438 

1376.02 

150  674 

339 

1065.00 

90259 

389 

1222.0S 

118  847 

439 

1379.16 

151  363 

340 

1068.14 

90792 

390 

1225.22 

119  459 

440 

1382.30 

152  053 

341 

1071.28 

91327 

391 

1228.36 

120  072 

441 

1385.44 

152  745 

342 

1074.42 

91863 

392 

1231.50 

120  687 

442 

1388.58 

153  439 

343 

1077.57 

92401 

393 

1234.65 

121  304 

443 

1391.73 

154  134 

344 

1080.71 

92941 

394 

1237.79 

121  922 

444 

1394.87 

154  830 

345 

1083.85 

93482 

395 

1240.93 

122  542 

445 

1398.01 

155  528 

346 

1086.99 

94025 

396 

1244.07 

123  163 

446 

1401.15 

156  228 

347 

1090.13 

94569 

397 

1247.21 

123  786 

447 

1404.29 

156  930 

348 

1093.27 

95115 

398 

1250.35 

124  410 

448 

1407.43 

157  633 

349 

1096.42 

95662 

399 

1253.50 

125  036 

449 

1410.58 

158  337 

350 

1099.56 

96211 

400 

1256.64 

125  664 

450 

1413.72 

159  043 

ClRCUMFERKNt'K 

and   Area   of   Circles. 

517 

j  Circum. 

Area. 

I'ircum. 

Area. 

Circum. 

Area. 

Diam- 

/*•—V 

^5^. 

Diam- 

/~*\ 

^g?|S. 

Diam- 

s~\ 

/T~v 

eter. 

P 

w 

Bfc  r. 

O 

w 

eter. 
551 

0 

Qj 

451 

1416.86 

159  751 

1573.94 

197136 

1731.02 

238  448 

452 

1420.00 

160  460 

502 

1577.08 

197  923 

17/.4.16 

239  314 

•i:.:1. 

1423.14 

161  171 

503 

1580.22 

198  713 

1737.40 

240  182 

454 

1426.28 

161  SS3 

504 

1583.36 

199  504 

1710.44 

241  051 

455 

1429.42 

162  597 

505 

1586.50 

200  296 

555 

1743.58 

241  922 

456 

1432.57 

163  313 

506 

1 589.65 

201090 

556 

1716.73 

242  795 

457 

1435.71 

164  030 

507 

1592.79 

201886 

557 

1749.87 

243  669 

458 

1438.85 

If.  1748 

508 

1595.93 

202  683 

558 

1753.01 

244  545 

459 

1441.99 

165  468 

509 

1599.07 

20:'!  1-2 

559 

1756.15 

245  422 

460 

1445.1:'. 

166  190 

510 

1602.21 

204  282 

560 

1759.29 

246  301 

461 

1448.27 

166  914 

511 

1605.35 

205  084 

561 

1762.43 

247  181 

462 

1451.42 

167  639 

512 

1608.50 

205  887 

562 

1765.58 

J  IS  063 

4C3 

1454.56 

168  365 

513 

1611.64 

206  692 

563 

1768.72 

248  947 

464 

1457.70 

169  093 

514 

1614.78 

207  499 

564 

1771.86 

249  832 

465 

1460.84 

169  85 

515 

1617.92 

208  307 

565 

1775.00 

250  719 

166 

1463.98 

170  55 1 

516 

1621.06 

209  117 

566 

1778.14 

251607 

467 

1467.12 

171287 

517 

1624.20 

209  928 

567 

1781.28 

252  497 

468 

1470.27 

172  021 

518 

1627.35 

210  741 

568 

1784.42 

253  388 

469 

1173.41 

172  757 

519 

1630.49 

211556 

569 

1787.57 

254  281 

470 

1476.55 

173  494 

520 

1633.63 

212  372 

570 

1790.71 

255176 

471 

1479.69 

174  234 

521 

1636.77 

213  189 

571 

1793.85 

256  072 

47-J 

14S2.83 

174  974 

522 

1639.91 

214  008 

572 

1796.99 

256  970 

473 

1485.97 

175  716 

523 

1643.05 

214  829 

573 

1800.13 

257  869 

474 

1489.11 

176  460 

524 

1646.20 

215  651 

574 

1803.27 

258  770 

475 

1492.26 

177  205 

525 

1649.34 

216  475 

575 

1806.42 

259  672 

476 

1495.40 

177  952 

526 

1652.48 

217  301 

576 

1S09.56 

260  576 

477 

1498.54 

178  701 

527 

1655.62 

218  128 

577 

1812.70 

261  482 

478 

1501.68 

179  451 

528 

165S.76 

218  956 

578 

1815.84 

262  389 

479 

1504.82 

180  203 

529 

1661.90 

219  787 

579 

1818.98 

263  298 

480 

1507.% 

ISO  956 

530 

1665.04 

220  618 

580 

1S22.12 

264  208 

481 

1511.11 

1-1  711 

531 

1668.19 

2-21  452 

581 

1825.27 

265120 

482 

1514.25 

182  467 

- 

1671.33 

222  287 

582 

182S.41 

266  033 

483 

1517.39 

1S3  225 

533 

1674.47 

22  1  123 

583 

1S31.55 

266  948 

484 

1520.53 

183  984 

534 

1677.61 

223  961 

584 

1834.69 

267  865 

485 

1523.67 

184  745 

535 

16S0.75 

•--'1801 

585 

1S37.83 

268  783 

486 

1526.81 

1-5  508 

536 

1683.89 

225642 

586 

1840.97 

269  702 

487 

1529.96 

186  272 

537 

1687.04 

226  484 

587 

1844.11 

270  624 

4- 

1533.10 

187  038 

538 

1690.18 

227  329 

588 

1847.26 

271547 

4- J 

1536.24 

1*7  805 

539 

1693.32 

-_-175 

589 

1850.40 

272  471 

490 

1539.38 

188  574 

540 

1696.46 

229  022 

590 

1853.54 

273  397 

491 

1542.52 

189  345 

541 

1699.60 

229  871 

591 

1856.68 

274  325 

492 

1545.66 

190  117 

512 

1702.74 

230  7-_ 

592 

1*59.82 

275  254 

493 

1548.81 

190  890 

543 

1705.88 

231574 

593 

1862.96 

276184 

494 

1551.95 

191665 

511 

1709.03 

232  428 

594 

1866.11 

277  117 

495 

1555.09 

192  4 12 

545 

1712.17 

233  283 

595 

1869.25 

278  051 

496 

1558.23 

193  223 

546 

1715..1 

234  140 

596 

187239 

278  986 

497 

1561.37 

194  000 

547 

171- 

234  998 

597 

1875.53 

279  923 

!■.'«• 

1564.51 

194  782 

548 

1721.59 

235  858 

598 

1-78.67 

280  862 

499 

1567.65 

195  565 

549 

1721.73 

236  720 

599 

1881.81 

281802 

500 

1. -.70.80 

196  350 

550 

1727.88 

287588    I 

,    600 

1884.% 

282  743 

518 

Circumference 

and  Area  of  Circles. 

Circum. 

Area. 

Circum. 

Area. 

Circum. 

Area. 

Diam- 

/■—N 

• 

Diam- 

/"\ 

>^HS^ 

Diam- 

/*->v 

^^. 

eter. 

o 

eter. 
651 

o 

w 

eter. 
701 

o 

w 

601 

1888.10 

283  687 

2045.18 

332  853 

2202.26 

385  945 

602 

1891.24 

284  631 

652 

2048.32 

333  876 

702 

2205.40 

387  047 

603 

1894.38 

285  578 

653 

2051.46 

334  901 

703 

2208.54 

388  151 

604 

1897.52 

286  526 

654 

2054.60 

335  927 

704 

2211.68 

389  256 

605 

1900.66 

287  475 

655 

2057.74 

336  955 

705 

2214.82 

390  363 

606 

1903.81 

288  426 

656 

2060.88 

337  985 

706 

2217.96 

391  471 

607 

1906.95 

289  379 

657 

2064.03 

339  016 

707 

2221.11 

392  580 

608 

1910.09 

290  333 

658 

2067.17 

340  049 

708 

2224.25 

393  692 

609 

1913.23 

291  289 

659 

2070.31 

341  083 

709 

2227.39 

394  805 

610 

1916.37 

292  247 

660 

2073.45 

342  119 

710 

2230.53 

395  919 

611 

1919.51 

293  206 

661 

2076.59 

343  157 

711 

2233.67 

397  035 

612 

1922.65 

294  166 

662 

2079.73 

344  196 

712 

2236.81 

398  153 

613 

1925.80 

295128 

663 

2082.88 

345  237 

713 

2239.96 

399  272 

614 

1928.94 

296  092 

664 

2086.02 

346  279 

714 

2243.10 

400  393 

615 

1932.08 

297  057 

665 

2089.16 

347  323 

715 

2246.24 

401  515 

616 

1935.22 

298  024 

666 

2092.30 

348  368 

716 

2249.38 

402  639 

617 

1938.36 

298  992 

667 

2095.44 

349  415 

717 

2252.52 

403  765 

618 

1941.50 

299  962 

668 

2098.58 

350  464 

718 

2255.66 

404  892 

619 

1944.65 

300  934 

669 

2101.73 

351  514 

719 

2258.81 

406  020 

620 

1947.79 

301  907 

670 

2104.87 

352  565 

720 

2261.95 

407  150 

621 

1950.93 

302  882 

671 

2108.01 

353  618 

721 

2265.09 

408  282 

622 

1954.07 

303  858 

672 

2111.15 

354  673 

722 

2268.23 

409  416 

623 

1957.21 

304  836 

673 

2114.29 

355  730 

723 

2271.37 

410  550 

624 

1960.35 

305  815 

674 

2117.43 

356  788 

724 

2274.51 

411  687 

625 

1963.50 

306  796 

675 

2120.58 

357  847 

725 

2277.65 

412  825 

626 

1966.64 

307  779 

676 

2123.72 

358  908 

726 

2280.80 

413  965 

627 

1969.78 

308  763 

677 

2126.86 

359  971 

727 

2283.94 

415  106 

628 

1972.92 

309  748 

678 

2130.00 

361  035 

728 

2287.08 

416  248 

629 

1976.06 

310  736 

679 

2133.14- 

362  101 

729 

2290.22 

417  393 

630 

1979.20 

311725 

680 

2136.28 

363  168 

730 

2293.36 

418  539 

631 

1982.35 

312  715 

681 

2139.42 

364  237 

731 

2296.50 

419  686 

632 

1985.49 

313  707 

682 

2142.57 

365  308 

732 

2299.65 

420  835 

633 

1988.63 

314  700 

683 

2145.71 

366  380 

733 

2302.79 

421  986 

634 

1991.77 

315  696 

684 

2148.85 

367  453 

734 

2305.93 

423  139 

635 

1994.91 

316  692 

685 

2151.99 

368  528 

735 

2309.07 

424  292 

636 

1998.05 

317  690 

686 

2155.13 

369  605 

736 

2312.21 

425  447 

637 

2001.19 

318  690 

687 

2158.27 

370  684 

737 

2315.35 

426  604 

638 

2004.34 

319  692 

688 

2161.42 

371  764 

738 

2318.50 

427  762 

639 

2007.48 

320  695 

689 

2164.56 

372  845 

739 

2321.64 

428  922 

640 

2010.62 

321  699 

690 

2167.70 

373  928 

740 

2324.78 

430  084 

641 

2013.67 

322  705 

691 

2170.84 

375  013 

741 

2327.92 

431  247 

642 

2016.90 

323  713 

692 

2173.98 

376  099 

742 

2331.06 

432  412 

643 

2020.04 

324  722 

693 

2177.12 

377  187 

743 

2334.30 

433  578 

644 

2023.19 

325  733 

694 

2180.27 

378  276 

744 

2337.34 

434  746 

645 

2026.33 

326  745 

695 

2183.41 

379  367 

745 

2340.49 

435  916 

646 

2029.47 

327  759 

696 

2186.55 

380  459 

746 

2343.63 

437  087 

647 

2032.61 

328  775 

697 

2189.69 

381  554 

747 

2346.77 

438  259 

648 

2035.75 

329  792  ' 

698 

2192.83 

382  649 

748 

2349.91 

439  433 

619 

2038.89 

330  810 

699 

2195.97 

383  746 

749 

2353.05 

440  609 

650 

2042.04 

331  831 

700 

2199.11 

384  845 

750 

2356.19 

441  786 

Circumference 

and   Area   of   Circles. 

519 

Circum. 

Area. 

Circum. 

Area. 

Circum. 

Area. 

Diam- 

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>^^5V 

Diani- 

S~\ 

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I'KUII- 

/~\ 

o 

eter. 

o 

w 

eter. 

801 

o 

o 

eti-r. 
851 

o 

751 

_     .'.34 

412  965 

2516.42 

503  912 

2673.50 

568  786 

752 

2362.48 

414  146 

- 

2519 

505  171 

2676.61 

570  121 

753 

2365.62 

11".  328 

- 

2.70 

506  432 

- 

2679.78 

571  463 

754 

_     -.76 

1 16  511 

804 

2525.84 

507  • 

B54 

2.92 

572  803 

755 

2371.90 

447  1    " 

-1  15 

2528.98 

508  958 

2686.06 

574  146 

756 

2375.04 

;;>SS3 

806 

2532.12 

510 

856 

2689.20 

575  490 

757 

2378.19 

'072 

25:;:,.  27 

511  490 

857 

2692.34 

576  835 

758 

2381.33 

451  262 

-   - 

253S.41 

512  758 

858 

2695.49 

578  182 

759 

23S4.47 

452453 

2541.55 

514  028 

859 

2698.63 

579  530 

760 

2387.61 

453  646 

810 

2544.69 

515  300 

860 

2701.77 

580  880 

761 

2390.75 

454  841 

811 

2547.83 

516  573 

861 

2704.91 

582  232 

762 

2393.89 

456  037 

812 

2550.97 

517  848 

2708.05 

583  585 

763 

2397.04 

457  234 

813 

2554.11 

519  124 

863 

2711.19 

584  940 

764 

2400.18 

458  4:34 

814 

2557.26 

520  402 

864 

2714.:'.! 

586  297 

765 

2403    - 

459  635 

815 

2560.40 

521  681 

865 

2717.48 

587  655 

766 

2406.46 

460  837 

816 

2563-54 

522  962 

866 

2720.62 

589  014 

767 

2409.60 

462  041 

817 

2566.68 

524  215 

867 

2723.76 

590  375 

768 

2412.74 

463  247 

818 

2569.82 

525  529 

868 

2726.90 

591738 

769 

2415.88 

464  454 

819 

2572.96 

526  814 

869 

2730.04 

593  102 

770 

2419.03 

465  663 

820 

•2576.11 

528  102 

870 

2733.19 

594  468 

771 

2422.17 

466  873 

821 

2579. -2-5 

529  391 

871 

2736.33 

595  835 

772 

2425.31 

468  085 

822 

2582.39 

530  681 

872 

2739.47 

597  204 

773 

2428.45 

469  298 

- 

2585.53 

531  973 

873 

2742.61 

598  575 

774 

2431.59 

470  513 

-21 

25S8.67 

533  267 

874 

2745.75 

599  947 

771 

2434.73 

471  730 

825 

2591.81 

534  562 

875 

27 13.89 

601  320 

776 

2437.88 

472  948 

826 

2594.96 

535  858 

876 

2752.04 

602  696 

777 

2441.02 

171  168 

327 

2£  18.10 

537  157 

877 

2755.18 

604  073 

77S 

2444.16 

475  389 

828 

2601.24 

538  456 

878 

2758.32 

605  451 

779 

2447.30 

476  612 

829 

2604.38 

539  758 

879 

2761.46 

606  831 

780 

24.50.44 

477  S36 

830 

2607.52 

541061 

880 

2764.60 

608  212 

781 

2453.58 

479  062 

831 

2610.66 

542  365 

881 

2767.74 

609  595 

782 

2456.73 

480  290 

832 

2613.81 

543  671 

882 

2770.88 

610  980 

783 

2459.87 

481  519 

833 

2616.95 

544  979 

883 

2774.03 

612  366 

7-1 

2463.01 

4-2  750 

834 

2620.09 

546  288 

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2777.17 

613  754 

7-5 

2466.15 

483  982 

835 

2623.23 

547  599 

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2780.31 

615  143 

786 

2469.29 

485  216 

836 

2626.37 

548  912 

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2783.45 

616  534 

787 

2472.1:; 

486  451 

837 

2629.51 

550  226 

887 

2786.59 

617  927 

788 

2175.58 

487  688 

838 

2632.65 

551  541 

s.S 

2789.73 

619  321 

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2478.72 

488  927 

B39 

2635.80 

552  858 

— .» 

2792.88 

620  717 

790 

2481.86 

490  167 

840 

3.94 

554  177 

890 

2796.02 

622  114 

791 

2485.00 

491409 

841 

2642.08 

555  497 

B91 

2799.16 

623  513 

792 

2488.14 

492  1 

842 

2645.22 

556  819 

892 

2802.30 

624  913 

793 

24 

493  897 

-.36 

5.5S  1 12 

893 

a  ..u 

626  315 

794 

2491. 12 

495  143 

B44 

2651.50 

1  " 

894 

2808.58 

627  718 

795 

24  17.57 

496  391 

B45 

1.65 

560794 

895 

2811.7' 

629  124 

796 

2500.71 

497  641 

846 

2657  " 

562  122 

896 

2814.87 

630  530 

498  E 

B47 

0.93 

152 

8  : 

2818.01 

631  938 

798 

2506.99 

500  1 15 

348 

1.07 

564  7-:: 

2821.15 

1     (348 

799 

2510.13 

501 

849 

7.23 

566  11'. 

2824.29 

1  760 

.v,,. 

2513.27 

2671 

150 

900 

178 

520 

Circumference 

and  Area  of  Circles. 

Circuru. 

Area. 

Circum. 

Area. 

Circufil, 

Area. 

Diam- 

S~\ 

/^H^ 

Diam- 

/~N 

i«rfSSS». 

Diam- 

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^wg. 

eter. 

o 

IP 

eter. 

o 

IP 

eter. 

o 

w 

901 

2830.58 

637  587 

934 

2934.25 

685  147 

967 

3037.92 

734  417 

902 

2833.72 

639  003 

935 

2937.39 

686  615 

968 

3041.06 

735  937 

903 

2836.86 

640  421 

936 

2940.53 

688  084 

969 

3044.20 

737  458 

904 

2840.00 

641840 

937 

2943.67 

689  555 

970 

3047.34 

738  981 

905 

2843.14 

643  261 

938 

2946.81 

691  028 

971 

3050.49 

740  506 

906 

2846.28 

644  683  . 

939 

2949.96 

692  502 

972 

3053.63 

742  032 

907 

2849.42 

646  107 

940 

2953.10 

693  978 

973 

3056.77 

743  559 

908 

2852.57 

647  533 

941 

2956.24 

695  455 

974 

3059.91 

745  088 

909 

2855.71 

648  960 

942 

2959.38 

696  934 

975 

3063.05 

746  619 

910 

2858.85 

650  388 

943 

2962.52 

698  415 

976 

3066.19 

748  151 

911 

2861.99 

651  818 

944 

2965.66 

699  897 

977 

3069.34 

749  685 

912 

2865.13 

653  250 

945 

2968.81 

701  380 

978 

3072.48 

751  221 

913 

2868.27 

654  684 

946 

2971.95 

702  865 

979 

3075.62 

752  758 

914 

2871.42 

656  118 

947 

2975.09 

704  352 

980 

3078.76 

■  754  296 

915 

2874.56 

657  555 

948 

2978.23 

705  840 

981 

3081.90 

755  837 

916 

2877.70 

658  993 

949 

2981.37 

707  330 

982 

3085.04 

757  378 

917 

2880.84 

660  433 

950 

2984.51 

708  822 

983 

3088.19 

758  922 

918 

2883.98 

661  874 

951 

2987.65 

710  315 

984 

3091.33 

760  466 

919 

2887.12 

663  317 

952 

2990.80 

711  809 

985 

3094.47 

762  013 

920 

2890.27 

664  761 

953 

2993.94 

713  307 

986 

3097.61 

763  561 

921 

2893.41 

666  207 

954 

2997.08 

714  803 

987 

3100.75 

765  111 

922 

2896.55 

667  654 

955 

3000.22 

716  303 

988 

3103.89 

766  662 

923 

2899.69 

669  103 

956 

3003.36 

717  804 

989 

3107.04 

768  215 

924 

2902.83 

670  554 

957 

3006.50 

719  306 

990 

3110.18 

769  769 

925 

2905.97 

672  006 

958 

3009.65 

720  810 

991 

3113.32 

771325 

926 

2909.11 

673  460 

959 

3012.79 

722  316 

992 

3116.46 

772  882 

927 

2912.26 

674  915 

960 

3015.93 

-  723  823 

993 

3119.60 

774  441 

928 

2915.40 

676  372 

961 

3019.07 

725  332 

994 

3122.74 

776  002 

929 

2918.54 

677  831 

962 

3022.21 

726  842 

995 

3125.88 

777  564 

930 

2921.68 

679  291 

963 

3025.35 

728  354 

996 

3129.03 

779128 

931 

2924.82 

680  752 

964 

3028.50 

729  867 

997 

3132.17 

780  693 

932 

2927.96 

682  216 

965 

3031.64 

731  382 

998 

3135.31 

782  260 

933 

2931.11 

683  680 

966 

3034.78 

732  899 

999 

3138.45 

783  828 

Note. — When  it  is  desired  to  find  the  circumference  corresponding  to 
any  diameter  not  in  the  table,  point  off  as  many  places  in  the  circumfer- 
ence as  have  been  pointed  off  in  the  diameter,  and  point  off  twice  as  many 
places  in  this  area  as  have  been  pointed  off  in  the  diameter.    Thus  : 


Hameters. 

Circumferences. 

Areas. 

9.16 

28.777 

65.8993 

91.6 

287.77 

6  589.93 

916. 

2877.7 

658  993. 

9160. 

28777. 

65  899  321. 

When  it  is  desired  to  find  the  circumference  or  area  for  any  diameter 
consisting  of  a  whole  number  and  a  decimal,  it  may  be  done  by  taking  the 
difference  between  the  tabular  figures  for  the  diameters  between  which 
the  given  diameter  lies  and  multiplying  this  difference  by  the  decimal  and 
adding  the  result  to  the  tabular  value  corresponding  to  the  next  lower 
diameter. 


POWERS    AND    ROOTS. 


Squares. 

Cubes. 

Number. 

»  Boota 

f  Roots. 

Keriprocals. 

1 

1 

1 

1.000  0000 

1.000  0000 

1.000  000  000 

2 

4 

8 

1.111  2136 

1.259  9210 

.500  000  000 

3 

9 

27 

1.732  0.508 

1.442  2496 

.333  333  333 

4 

16 

64 

2.000  0000 

1.587  4011 

.250  000  000 

5 

25 

125 

2.236  06S0 

L709  9759 

.200  000  000 

6 

36 

216 

2.449  4897 

1.8171206 

.166  666  667 

7 

49 

343 

2.645  7513 

1.912  9312 

.142  857  143 

8 

64 

512 

2.828  4271 

2.000  0000 

.125  000  000 

9 

Bl 

729 

3.000  0000 

2.0S0  0837 

.111  111  111 

10 

100 

1000 

3.162  2777 

2.154  4317 

.100  000  000 

11 

121 

1331 

3.316  6248 

2.223  9801 

.090  909  091 

12 

144 

1728 

3.464  1016 

2.289  4286 

.083  333  333 

13 

169 

2  197 

3.605  5513 

2.3,51  3347 

.076  923  077 

14 

196 

2  744 

3.741  6574 

2.4101422 

.071  428  571 

15 

225 

3  375 

3.872  9833 

2.466212] 

.066  666  667 

16 

256 

4  096 

4.000  0000 

2.5198421 

.062  500  000 

17 

289 

4  913 

4.123  10.56 

2.571  2816 

.0.58  823  529 

18 

324 

5  832 

4.242  6407 

2.620  7414 

.055  555556 

19 

361 

6  859 

4.358  - 

2.668  401 6 

.052  631  579 

20 

400 

8000 

4.472  1360 

2.714  4177 

.050  000  000 

21 

441 

9  261 

4.582  5757 

2.7.58  9243 

.047  619  048 

22 

484 

10  648 

4.690  4158 

2.802  0393 

.045  454  545 

23 

529 

12  167 

4.795  8315 

2.843  8670 

.043  478  261 

24 

576 

13  824 

4.898  9795 

2.884  4991 

.041  666  667 

25 

625 

15625 

5.000  0000 

2.924  0177 

.040  000  000 

26 

676 

17  576 

5.099  0195 

2.962  4960 

.038  461  538 

27 

729 

19  683 

5.196  1524 

3.000  0000 

.037  037  037 

28 

784 

21  952 

5.291  5026 

3.036  5889 

.035  714  286 

29 

841 

24  389 

.  5.3851648 

3.072  3168 

.034  482  759 

30 

900 

27  000 

5.477  2256 

3.107  232-5 

.033  333  333 

31 

961 

29  791 

5.567  7644 

3.141  3806 

.032  258  065 

32 

1024 

32  768 

5.656  8542 

3.174  8021 

.031  250  000 

33 

1089 

35  937 

5.744  5626 

3.207  5343 

.030  303  030 

34 

1  156 

39  304 

5.830  9519 

3.239  6118 

.029  411  765 

35 

1225 

42  875 

5.916  0798 

3.271  0663 

.028  571  429 

36 

1296 

46  656 

6.000  0000 

3.301  9272 

37 

1369 

50  6-53 

6.082  7625 

3.332  2218 

.027  027  027 

38 

1444 

54  872 

6.164  4140 

3.3619751 

.026  315  789 

39 

1  r.21 

59  319 

6.244  9980 

3.391  2114 

.025  641  026 

40 

1600 

64  000 

6.324  5553 

3.419  9519 

.025  000  000 

41 

1681 

68  921 

6.403  1242 

3.448  21 72 

.024  390  244 

42 

1  764 

74  088 

6.4S0  7407 

3.476  0266 

.023  809  524 

43 

1849 

79  507 

6.557  4385 

3.503  3981 

.023  255  SI 4 

11 

1936 

85184 

6.633  2496 

3.530  3483 

.022  727  273 

45 

2  025 

91  125 

6.708  2039 

3.556  8933 

.022  222  2*2 

46 

2  116 

97  336 

6.782  3300 

3.5.S3  0479 

.021  739  130 

47 

2209 

103  • 

6.8556546 

3.608  8261 

.021  276  600 

4* 

2  304 

110  592 

6.928  2032 

3.634  2411 

.020  833  333 

49 

2  101 

117  649 

7.000  0000 

3.659  3057 

.020  408  163 

50 

2500 

125  000 

7.0710'"- 

3.684  0314 

.020  000  000 

51 

2  601 

132  651 

7.1414284 

3.708  4298 

.019  607  843 

52 

2  704 

140  608 

7.211  1026 

3.732  5111 

.019  230  769 

.-.-'  1 


522 


Powers  and  Roots. 


Squares. 

Cubes. 

Number. 

V  Roots. 

f  Roots. 

Reciprocals. 

53 

2  809 

148  877 

7.280  1099 

3.756  2858 

.018  867  925 

54 

2  916 

157  464 

7.348  4692 

3.779  7631 

.018  518  519 

55 

3  025 

166  375 

7.416  1985 

3.802  9525 

.018  181  818 

56 

3  136 

175  616 

7.483  3148 

3.825  8624 

.017  857  143 

57 

3  249 

185  193 

7.549  8344 

3.848  5011 

.017  543  860 

58 

3  364 

195  112 

7.615  7731 

3.870  8766 

.017  241  379 

59 

3  481 

205  379 

7.681 1457 

3.892  9965 

.016  949  153 

60 

3  600 

216  000 

7.745  9667 

3.914  8676 

.016  666  667 

61 

3  721 

226  981 

7.810  2497 

3.930  4972 

.016  393  443 

62 

3  844 

238  328 

7.874  0079 

3.957  8915 

.016  129  032 

63 

3  969 

250  047 

7.937  2539 

3.979  0571 

.015  873  016 

64 

4  096 

262  144 

8.000  0000 

4.000  0000 

.015  625  000 

65 

4  225 

274  625 

8.062  2577 

4.020  7256 

.015  384  615 

66 

4  356 

287  496 

8.124  0384 

4.041  2401 

.015  151  515 

67 

4  489 

300  763 

8.185  3528 

4.061  5480 

.014  925  373 

68 

4  624 

314  432 

8.246  2113 

4.081  6551 

.014  705  882 

69 

4  761 

328  509 

8.306  6239 

4.101  5661 

.014  492  754 

70 

4  900 

343  000 

8.366  6003 

4.121  2853 

.014  285  714 

71 

5  041 

357  911 

8.426  1498 

4.140  8178 

.014  084  517 

72 

5184 

373  248 

8.485  2814 

4.160  1676 

.013  888  889 

73 

5  329 

389  017 

8.544  0037 

4.179  3390 

.013  698  630 

74 

5  476 

405  224 

8.602  3253 

4.198  3364 

.013  513  514 

75 

5  625 

421  875 

8.660  2540 

4.217  1633 

.013  333  333 

76 

5  776 

438  976 

8.717  7979 

4.235  8236 

.013  157  895 

77 

5  929 

456  533 

8.774  9644 

4.254  3210 

.012  987  013 

78 

6  084 

474  552 

8.831  7609 

4.272  6586 

.012  820  513 

79 

6  241 

493  039 

8.888  1944 

4.290  8404 

.012  658  228 

80 

6  400 

512  000 

8.944  2719 

4.308  8695 

.012  500  000 

81 

6  561 

531441 

9.000  0000 

4.326  7487 

.012  345  679 

82 

6  724 

551  368 

9.055  3851 

4.344  4815 

.012  195  122 

83 

6  889 

571  787 

9.110  4336 

4.362  0707 

.012  048  193 

84 

7  056 

592  704 

9.165  1514 

4.379  5191 

.011  904  762 

85 

7  225 

614  125 

9.219  5445 

4.396  8296 

.011  764  706 

86 

7  396 

636  056 

9.273  6185 

4.414  0049 

.011  627  907 

87 

7  569 

658  503 

9.327  3791 

4.431  0476 

.011  494  253 

88 

7  744 

681  472 

9.380  8315 

4.447  9692 

.011  363  636 

89 

7  921 

704  969 

9.433  9811 

4.464  7451 

.011  235  955 

90 

8  100 

729  000 

9.486  8330 

4.481  4047 

.011  111  111 

91 

8  281 

753  571 

9.539  3920 

4.497  9414 

.010  989  011 

92 

8  464 

778  688 

9.591  6630 

4.514  3574 

.010  869  565 

93 

8  649 

804  357 

9.643  6508 

4.530  6549 

.010  752  688 

94 

8  836 

830  584 

9.695  3597 

4.546  8359 

.010  638  298 

95 

9  025 

857  375 

9.746  7943 

4.562  9026 

.010  526  316 

96 

9  216 

884  736 

9.797  9590 

4.578  8570 

.010  416  667 

97 

9  409 

912  673 

9.848  8578 

4.594  7009 

.010  309  278 

98 

9  604 

941  192 

9.899  4949 

4.610  4363 

.010  204  082 

99 

9  801 

970  299 

9.949  8744 

4.626  0650 

.010  101  010 

100 

10  000 

1  000  000 

10.000  0000 

4.641  5888 

.010  000  000 

101 

10  201 

1  030  301 

10.049  8756 

4.657  0095 

.009  900  990 

102 

10  404 

1  061  208 

10.099  5049 

4.672  3287 

.009  803  922 

103 

10  609 

1  092  727 

10.148  8916 

4.687  5482 

.009  708  738 

104 

10  816 

1  124  864 

10.198  0390 

4.702  6694 

.009  615  385 

Powers 

and  Roots 

• 

Number. 

Squar.-. 

("ni  - 

^Roots. 

t      It.H-t*. 

Reciprocals. 

105 

11025 

1 157  625 

10.246  9508 

4.717  6940 

.009  523  810 

106 

11236 

1  191  016 

10.295  6:501 

4.732  6235 

.009  433  962 

107 

11449 

1  225  04:? 

10.344  0804 

1.747  4594 

.009  345  794 

108 

11664 

1  259  712 

10.392  3048 

4.762  2032 

.009  259  259 

109 

11881 

1  295  029 

10.440  3065 

1.776  8562 

.009  171  312 

110 

12100 

1331000 

10.488  0885 

4.791  4199 

.009  090  909 

111 

12  321 

1  367  631 

10.535  6538 

4.805  8995 

.009  009  009 

112 

12  544 

1  404  928 

10.583  0052 

4.820  2845 

.008  928571 

113 

12  769 

1  442  897 

10.630  1458 

4.834  5881 

.008  819  558 

114 

12  996 

1  4S1  544 

10.677  0783 

4.848  8076 

.008  771  930 

115 

13  225 

1  520  875 

10.723  8053 

4.862  9442 

.008  695  652 

116 

13  456 

1560  896 

10.770  3296 

4.876  9990 

.008  620  690 

117 

13  689 

1  601  613 

10.816  6538 

4.890  97: '.2 

.008  547  009 

118 

13  924 

1  643  032 

10.862  7805 

4.904  8681 

.008  474  576 

119 

14  161 

1685159 

10.908  7121 

4.918  6.847 

.008  403  361 

120 

14  400 

1728  000 

10.9.54  4512 

4.932  4212 

.008  333  333 

121 

14  641 

1  771  561 

11.000  0000 

4.946  0874 

.008  264  463 

122 

14  884 

1  815  848 

11.045  3610 

4.959  67.">7 

.008  196  721 

123 

15129 

1860  867 

11.090  5365 

4.973  1898 

.008  130  081 

124 

15  376 

1  906  624 

11.135  5287 

4.986  6310 

.008  064  516 

125 

15  625 

1  953  125 

11.180  3399 

5.000  0000 

.008  000  000 

126 

15  876 

2  000  376 

11.224  972-2 

5.013  2979 

.007  936  508 

127 

16129 

2  048  383 

11.269  4277 

5.026  5257 

.007  874  016 

128 

16  384 

2  097  152 

11.313  7085 

5.039  6842 

.007  812  500 

129 

16  641 

2  146  689 

11.357  8167 

5.052  7743 

.007  751  938 

130 

16  900 

2197  000 

11.401  7543 

5.065  7970 

.007  692  308 

131 

17  161 

2  248  091 

11.445  5231 

5.078  7531 

.007  633  588 

132 

17  424 

2  299  968 

11.489  1253 

5.091  6434 

.007  575  758 

133 

17  689 

2  352  637 

11.532  5626 

5.104  4687 

.007  518  797 

134 

17  956 

2  406  104 

11.575  8369 

5.117  2299 

.007  462  687 

135 

18  225 

2  460  375 

11.618  9500 

5.129  9278 

.007  407  407 

136 

18  496 

2  515  456 

11.661  9038 

5.142  5632 

.007  352  941 

137 

18  769 

2  571  353 

11.704  6999 

5.155  1367 

.007  299  270 

l:> 

19  044 

2  628  072 

11.747  3401 

5.167  6493 

.007  246  377 

139 

19  321 

2  685  619 

11.789  8261 

5.180  1015 

.007  194  245 

140 

19  600 

2  744  000 

11.832  1596 

5.192  4941 

.007  142  857 

141 

19  881 

2  803  221 

11.874  3421 

5.204  8279 

.007  092  199 

142 

20164 

2  863  288 

11.916  3753 

5.217  1031 

.007  042  254 

143 

20  449 

2  924  207 

11.9.58  2607 

5.229  3215 

.006  993  007 

144 

20  736 

2  985  984 

12.000  0000 

5.241  4828 

.006  944  444 

145 

21025 

3  048  625 

12.041  5946 

5.253  5879 

.006  896  552 

146 

21316 

3  112  136 

12.0S3  0460 

5.265  6374 

.006  849  315 

1 17 

21609 

3  176  523 

12.124  3557 

5.277  6321 

.006  802  721 

148 

21904 

3  241792 

12.165  5251 

5.289  5725 

.006  7-V.  757 

149 

22  201 

3  307  949 

12.206  5556 

5.301  1592 

.006  711  409 

150 

22.500 

3  375  000 

12.247  4487 

5.313  2928 

.006  666  667 

151 

22  801 

3  442  951 

12.288  2057 

5.3250740 

.006  622  517 

152 

23  104 

3  511  008 

12.328  8280 

5.336  8033 

.006578947 

153 

23  409 

3  581  577 

12,3693169 

5.348  4812 

.006  535  948 

1.54 

23  716 

3652264 

12.4096736 

5.360  1084 

.006  493  506 

155 

J I  025 

3  723  875 

12.119  8996 

5.371  6854 

.006  451  613 

156 

24 

3  796  416 

12.489  9960 

5.3832126 

.006  110256 

524 

Powers 

and  Roots 

• 

Squares. 

Cubes. 

f  Roots. 

Number. 

y  Roots. 

Reciprocals. 

157 

24  649 

3  869  893 

12.529  9641 

5.394  6907 

.006  369  427 

158 

24  964 

3  944  312 

12.569  8051 

5.406  1202 

.006  329  114 

159 

25  281 

4  019  679 

12.609  5202 

5.417  5015 

.006  289  308 

160 

25  600 

4  096  000 

12.649  1106 

5.428  8352 

.006  250  000 

161 

25  921 

4  173  281 

12.688  5775 

5.440  1218 

.006  211 180 

162 

26  244 

4  251  528 

12.727  9221 

5.451  3618 

.006  172  840 

163 

26  569 

4  330  747 

12.767  1453 

5.462  5556 

.006  134  969 

164 

26  896 

4  410  944 

12.806  2485 

5.473  7037 

.006  097  561 

165 

27  225 

4  492  125 

12.845  2326 

5.484  8066 

.006  060  606 

166 

27  556 

4  574  296 

12.884  0987 

5.495  8647 

.006  024  096 

167 

27  889 

4  657  463 

12.922  8480 

5.506  8784 

.005  988  024 

168 

28  224 

4  741  632 

12.961  4S14 

5.517  8484 

.005  952  381 

169 

28  561 

4  826  809 

13.000  0000 

5.528  7748 

.005  917  160 

170 

28  900 

4  913  000 

13.038  4048 

5.539  6583 

.005  8S2  353 

171 

29  241 

5  000  211 

13.076  6968 

5.550  4991 

.005  847  953 

172 

29  584 

5  088  448 

13.114  8770 

5.561  2978 

.005  813  953 

173 

29  929 

5  177  717 

13.152  9464 

5.572  0546 

.005  780  347 

174 

30  276 

5  268  024 

13.190  9060 

5.582  7702 

.005  747  126 

175 

30  625 

5  359  375 

13.228  7566 

5.593  4447 

.005  714  286 

176 

30  976 

5  451  776 

13.266  4992 

5.604  0787 

.005  681  818 

177 

31329 

5  545  233 

13.304  1347 

5.614  6724 

.005  649  718 

178 

31684 

5  639  752 

13.341  6641 

5.625  2263 

.005  617  978 

179 

32  041 

5  735  339 

13.379  0882 

5.635  7408 

.005  586  592 

180 

32  400 

5  832  000 

13.416  4079 

5.646  2162 

.005  555  556 

181 

32  761 

5  929  741 

13.453  6240 

5.656  6528 

.005  524  862 

182 

33  124 

6  028  568 

13.490  7376 

5.667  0511 

.005  494  505 

183 

33  489 

6  128  487 

13.527  7493 

5.677  4114 

.005  464  481 

184 

33  856 

6  229  504 

13.564  6600 

5.687  7340 

.005  434  783 

185 

34  225 

6  331  625 

13.601  4705 

5.698  0192 

.005  405  405 

186 

34  596 

6  434  856 

13.638  1817 

5.708  2675 

.005  376  344 

187 

34  969 

6  539  203 

13.674  7943 

5.718  4791 

.005  347  594 

188 

35  344 

6  644  672 

13.711  3092 

5.728  6543 

.005  319  149 

189 

35  721 

6  751  269 

13.747  7271 

5.738  7936 

.005  291  005 

190 

36  100 

6  859  000 

13.784  0488 

5.748  8971 

.005  263  158 

191 

36  481 

6  967  871 

13.820  2750 

5.758  9652 

.005  235  602 

192 

36  864 

7  077  888 

13.856  4065 

5.768  9982 

.005  208  333 

193 

37  249 

7  189  517 

13.892  4400 

5.778  9966 

.005  181  347 

194 

37  636 

7  301  384 

13.928  3883 

5.788  9604 

.005  154  639 

195 

38  025 

7  414  875 

13.964  2400 

5.798  8900 

.005  128  205 

196 

38  416 

7  529  536 

14.000  0000 

5.808  7857 

.005  102  041 

197 

38  809 

7  645  373 

14.035  6688 

5.818  6479 

.005  076  142 

198 

39  204 

7  762  392 

14.071  2473 

5.828  4867 

.005  050  505 

199 

39  601 

7  880  599 

14.106  7360 

5.838  2725 

.005  025  126 

200 

40  000 

8  000  000 

14.142  1356 

5.848  0355 

.005  000  000 

201 

40  401 

8  120  601 

14.177  4469 

5.857  7660 

.004  975  124 

202 

40  804 

8  242  408 

14.212  6704 

5.867  4673 

.004  950  495 

203 

41209 

8  365  427 

14.247  8068 

5.877  1307 

.004  926  108 

201 

41616 

8  489  664 

14.282  8569 

5.886  7653 

.004  901  961 

205 

42  025 

8  615  125 

14.317  8211 

5.896  3685 

.004  878  049 

206 

42  436 

8  741  816 

14.352  7001 

5.905  9406 

.004  854  369 

207 

42  849 

8  869  743 

14.387  4946 

5.915  4817 

.004  830  918 

208 

43  264 

8  998  912 

14.422  2051 

5.924  9921 

.004  807  692 

Towers   anp  Roots. 


52* 


Number. 

Squares. 

('ill-  9. 

1  B 

l  i:..ots. 

Recipro 

209 

43  631 

9  129  329 

14.456  8 

5.934  1721 

.004  784 

210 

11100 

9  2G1  000 

14.491  3767 

5.943  9220 

701  905 

211 

44  521 

9  393  931 

1 1.525  B 

5.953  3418 

1  739  336 

212 

44  944 

9  528  1 

11.560  2198 

162  7320 

.      1  716  981 

213 

45 

9  063  5.  7 

14.594  5195 

72  0926 

.004  694  836 

211 

4".  7% 

9  800  34 1 

11.028  7 

5.981  4210 

.00-1  672  897 

215 

46  - 

9  93S  375 

11. 

5.990  7264 

.004  051  103 

46  • 

lit  077' 

14.6%  9385 

6.000  0000 

.004  029  630 

217 

47  0S9 

10  218  313 

11.730  9199 

6.009  24.50 

.004  608  "295 

218 

47524 

10  360  232 

14.7648231 

6.0184617 

.004  587  1.56 

219 

47  961 

10  503  459 

11.798  6486 

6.027  6502 

.004  566  210 

220 

48  400 

10  648  000 

14.832  3970 

6.036  8107 

.004  545  155 

•2-21 

48  841 

10  793  861 

14.866  0687 

6.045  9435 

.004  524  887 

222 

49  281 

10  911  048 

14.899  6644 

6.055  0489 

.001  504  505 

223 

49  7 

11  0S9  567 

14.933  1845 

6.004  1270 

.004  484  305 

224 

50 17-; 

11  239  424 

14.966  6 

6.073  1779 

.004  464  286 

22.'. 

50  625 

il  390  625 

15.000  0000 

6.0S2  4020 

.004  414  141 

226 

51  076 

11  543  176 

15.033  2964 

0.099  1994 

.004  424  779 

2-27 

51  529 

11  007  083 

15.066  5192 

6.100  1702 

.004  405  286 

228 

51  984 

11  - 

15.099  6689 

6.1091147 

.004  3.85  965 

229 

52  441 

12  008  9S9 

15.132  7460 

6.1180332 

.004  366  812 

230 

52  900 

12  167  000 

15.165  7509 

0.120  9257 

.001347  B26 

231 

301 

12  326  391 

15.198  1 

6.135  7924 

.004  329  004 

232 

53SJ1 

12  487  1    • 

15.2315462 

6.144  6337 

.004  310  315 

233 

54  289 

12  649:.  7 

15.204  : 

0.153  4495 

.004  291  - 15 

234 

•M756 

12812  904 

15.297  05S5 

6.162  2401 

.004  273  .504 

233 

55  25 

12  977  87o 

15.329  7097 

0.171  0 

.004  255  319 

236 

55  096 

13  144  256 

15.362  2915 

0.179  7406 

.004  237  288 

237 

56  169 

13  312  053 

15.394  8043 

6.188  4028 

.004  219  409 

238 

56  614 

13  481  272 

15.427  2486 

0.197  1544 

.004  201  681 

239 

57  121 

13  651  919 

15.4596248 

0.2058218 

.004  184  100 

240 

57  600 

13  824  000 

15.491  9334 

0.214  4050 

.004  166  607 

241 

58  081 

13  997  521 

15.5241747 

6.223  0843 

.004  149  378 

242 

58.564 

11172  488 

15.556  3492 

0.231  0797 

.004  132  231 

59  049 

1 1  348  907 

15.588  4573 

6.240  2515 

.004  115  226 

241 

59  536 

14526784 

15.6204994 

6.248  7998 

.004  098  361 

245 

60  025 

14  70612.-) 

15.652  1758 

0.257  32 is 

.004  081  633 

246 

60  516 

1 1  8S6  936 

15.684  3871 

0.26-5  8260 

.004  065  041 

247 

61009 

1 5  069  223 

15.7162 

0.274  3054 

.004  048  583 

248 

61504 

15  252  992 

15.7480157 

0.282  701:: 

.004  032  2.58 

249 

62  001 

15  4::s  249 

15.779  7     • 

6.291 1940 

.001  016  064 

250 

62  500 

15  625  000 

15.811  i 

0.299  & 

.004  000  000 

251 

63  001 

15  813  251 

15.842  9" 

0.307  9935 

.003  984  004 

252 

63  504 

16  003  003 

15.8745079 

6.310  3590 

.003  908  251 

2-53 

04  009 

16194  277 

15.905 

■     J 17035 

.003  952  509 

254 

64  516 

16  3S7  064 

15.! 

.003  937  008 

255 

65  025 

16  581  375 

15.9687194 

0.341  3S 

.003  921  509 

256 

65  536 

16  777  216 

16.000  0000 

6.349  0042 

.003  900  250 

257 

66  049 

16  974  593 

16.031  2195 

6.357  80 11 

.003  891  "1 

258 

66  564 

17173512 

16.062! 

0. 306  0968 

.003  87" 

259 

67081 

17  373  979 

16.093  4769 

6.374  3111 

.003  801  004 

260 

67  600 

17  576  000 

16.124  6155 

6.382  5043 

.003846154 

526 

Powers 

and  Roots 

Squares. 

Cubes. 

1X  Roots. 

Number. 

f  Roots. 

Reciprocals. 

261 

68121 

17  779  581 

16.155  4944 

6.390  6765 

.003  831  418 

262 

68  644 

17  984  728 

16.186  4141 

6.398  8279 

.003  816  794 

263 

69169 

18  191  447 

16.217  2747 

6.406  9585 

.003  802  281 

264 

69  696 

18  399  744 

16.248  0768 

6.415  0687 

.003  7S7  879 

265 

70  225 

18  609  625 

16.278  8206 

6.423  1583 

.003  773  585 

266 

70  756 

18  821  096 

16.309  5064 

6.431  2276 

.003  759  398 

267 

71289 

19  034  163 

16.340  1346 

6.439  2767 

.003  745  318 

268 

71824 

19  248  832 

16.370  7055 

6.447  3057 

.003  731  343 

269 

72  361 

19  465  109 

16.401  2195 

6.455  3148 

.003  717  472 

270 

72  900 

19  683  000 

16.431  6767 

6.463  3041 

.003  703  704 

271 

73  441 

19  902  511 

16.462  0776 

6.471  2736 

.003  690  037 

272 

73  984 

20  123  643 

16.492  4225 

6.479  2236 

.003  676  471 

273 

74  529 

20  346  417 

16.522  7116 

6.487  1541 

.003  663  004 

274 

75  076 

20  570  824 

16.552  9454 

6.495  0653 

.003  649  635 

275 

75  625 

20  796  875 

16.583  1240 

6.502  9572 

.003  636  364 

276 

76176 

21  024  576 

16.613  2477 

6.510  8300 

.003  623  188 

277 

76  729 

21  253  933 

16.643  3170 

6.518  6839 

.003  610  108 

278 

77  284 

21  484  952 

16.673  3320 

6,526  5189 

.003  597  122 

279 

77  841 

21  717  639 

16.703  2931 

6.534  3351 

.003  584  229 

280 

78  400 

21  952  000 

16.733  2005 

6.542  1326 

.003  571  429 

281 

78  961 

22  188  041 

16.763  0546 

6.-549  9116 

.003  558  719 

282 

79  524 

22  425  768 

16.792  8556 

6.557  6722 

.003  546  099 

283 

80  089 

22  665  187 

16.822  6038 

6.565  4144 

.003  533  569 

284 

80  656 

22  906  304 

16.852  2995 

6.573  1385 

.003  521 127 

285 

81225 

23  149  125 

16.881  9430 

6.580  8443 

.003  508  772 

286 

81796 

23  393  656 

16.911  5345 

6.588  5323  ' 

.003  496  503 

287 

82  369 

23  639  903 

16.941  0743 

6.596  2023 

.003  484  321 

288 

82  944 

23  887  872 

16.970  5627 

6.603  8545 

.003  472  222 

289 

83  521 

24  137  569 

17.000  0000 

6.611  4890 

.003  460  208 

290 

84  100 

24  389  000 

17.029  3864 

6.619  1060 

.003  448  276 

291 

84  681 

24  642  171 

17.058  7221 

6.626  7054 

.003  436  426 

292 

85  264 

24  897  088 

17.088  0075 

6.634  2874 

.003  424  658 

293 

85  849 

25  153  757 

17.117  2428 

6.641  8522 

.003  412  969 

294 

86  436 

25  412  184 

17.146  4282 

6.649  3998 

.003  401  361 

295 

87  025 

25  672  375 

17.175  5640 

6.656  9302 

.003  389  831 

296 

87  616 

25  934  836 

17.204  6505 

6.664  4437 

.003  378  378 

297 

'  88  209 

26  198  073 

17.233  6879 

6.671  9403 

.003  367  003 

298 

88  804 

26  463  592 

17.262  6765 

6.679  4200 

.003  355  705 

299 

89  401 

26  730  899 

17.291  6165 

6.686  8831 

.003  344  482 

300 

90  000 

27  000  000 

17.320  5081 

6.694  3295 

.003  333  333 

301 

90  601 

27  270  901 

17.349  3516 

6.701  7593 

.003  322  259 

302 

91204 

27  543  608 

17.378  1472 

6.709  1729 

.003  311  258 

303 

91809 

27  818  127 

17.406  8952 

6.716  5700 

.003  301  330 

304 

92  416 

28  094  464 

17.435  5958 

6.723  9508 

.003  289  474 

305 

93  025 

28  372  625 

17.464  2492 

6.731  3155 

.003  278  689 

306 

93  636 

28  652  616 

17.492  8557 

6.738  6641 

.003  267  974 

307 

94  249 

28  934  443 

17.521  4155 

6.745  9967 

.003  257  329 

308 

94  864 

29  218  112 

17.549  9288 

6.753  3134 

.003  246  753 

309 

95  481 

29  503  609 

17.578  3958 

6.760  6143 

.003  236  246 

310 

96100 

29  791  000 

17.606  8169 

6.767  8995 

.003  225  806 

311 

96  721 

30  080  231 

17.635  1921 

6.775  1690 

.003  215  434 

312 

97  341 

30  371  328 

17.663  5217 

6.782  4229 

.003  205  128 

Towers 

and  Roots 

527 

Bqnares. 

Cubes. 

f  Hoots. 

Number. 

V  Roots. 

Reciprocals. 

313 

97  909 

30  664  297 

17.691  8060 

6.789  6613 

.003  194  888 

314 

98  596 

30  959  144 

17.7200451 

6.796  8s  1 1 

.003  184  713 

315 

99  22S 

31  255  875 

17.748  2393 

6.804  0921 

.003  174  603 

316 

99  856 

31  554  496 

17.776  3888 

6.811  2847 

.003  164  557 

317 

100  489 

31855  013 

17.S04  4938 

6.818  4620 

.003  1.54  574 

318 

101  124 

32  157  432 

17.S32  5545 

6.8256242 

.003  144  654 

319 

101  70 1 

32  461  759 

17.860  5711 

6.832  7711 

.003  134  796 

320 

102  400 

32  768  000 

17.8S8  5438 

6.839  9037 

.003  125  000 

321 

103  011 

33  076  161 

17.916  4729 

6.847  0213 

.003  115  265 

32-2 

103  68 1 

33  386  248 

17.944  3584 

6.854  1240 

.003  105  590 

323 

104  329 

33  698  267 

17.972  2008 

6.861  2120 

.003  095  975 

324 

104  976 

34  012  221 

18.000  0000 

6.868  2855 

.003  086  420 

325 

105  625 

34  328  125 

18.027  756 1 

6.875  3433 

.003  076  923 

326 

106  276 

34  645  976 

18.055  4701 

6.882  3S88 

.003  067  485 

327 

106  929 

34  965  7S3 

18.083  1413 

6.889  4188 

.003  048  104 

328 

107  584 

35  2S7  552 

18.110  7703 

6.896  4345 

.003  048  780 

329 

108  241 

35  611  289 

18.138  3571 

6.903  4359 

.003  039  514 

330 

108  900 

35  937  000 

18.165  9021 

6.910  4232 

.003  030  303 

331 

109  561 

36  264  691 

18.193  4054 

6.917  3964 

.003  021 148 

332 

110  224 

36  594  368 

18.220  8672 

6.924  3556 

.003  012  048 

333 

110  889 

36  926  037 

18.248  2876 

6.931  3088 

.003  003  003 

334 

111556 

37  259  704 

18.275  6069 

6.938  2321 

.002  994  012 

335 

112  225 

37  595  375 

18.303  0052 

6.945  1496 

.002  985  075 

336 

112  896 

37  933  056 

18.330  3028 

6.952  0533 

.002  976  190 

337 

113  569 

38  272  753 

18.357  5598 

6.958  9434 

.002  967  359 

338 

114  244 

38  614  472 

18.384  7763 

6.965  8198 

.002  958  580 

339 

114  921 

38  958  219 

18.411  9526 

6.972  6826 

.002  949  853 

340 

115  600 

39  304  000 

18.439  0889 

6.979  5321 

.002  941 176 

341 

116  281 

39  651  821 

18.466  1853 

6.986  3681 

.002  932  551 

342 

116  964 

40  001  688 

18.493  2420 

6.993  1906 

.002  923  977 

343 

117  649 

40  353  607 

18.520  2592 

7.000  0000 

.002  915  452 

344 

US  336 

40  707  584 

18.547  2370 

7.006  7962 

.002  906  977 

345 

119  025 

41  003  625 

18.574  1756 

7.013  5791 

.002  898  551 

346 

119  716 

41  421  736 

18.601  0752 

7.020  3490 

.002  890  173 

347 

120  409 

41  781  923 

18.627  9360 

7.027  1058 

.002  881  844 

348 

121  104 

42  144  192 

18.654  7581 

7.033  8497 

.002  873  563 

349 

121  801 

42  508  549 

18.681  5417 

7.040  5860 

.002  865  330 

350 

122  500 

42  875  000 

18.708  2869 

7.047  2987 

.002  857  143 

351 

123  201 

43  243  551 

18.734  9940 

7.054  0041 

.002  849  003 

352 

123  904 

43  614  208 

18.761  6630 

7.060  6967 

.002  840  909 

353 

124  609 

43  986  977 

18.788  2942 

7.067  3767 

.002  832  861 

354 

125  316 

44  301  864 

18.814  8877 

7.074  0440 

.002  824  859 

355 

126025 

4 1  738  875 

18.811  4437 

7.0S0  6988 

.002  816  901 

356 

126  7.''. 

45  118  016 

18.807  9623 

7.087  3411 

.002  808  989 

357 

127  449 

45  499  293 

1 3.894  4130 

7.093  9709 

.002  801120 

358 

128164 

45  8S2  712 

18.920  8^7'j 

7.100  5.885 

.002  793  2% 

359 

128  881 

40  208  279 

is. 'J  17  'J'.'.".:'. 

7. 107  1937 

.002  785  515 

360 

129  600 

46  656  000 

18.9736660 

7.113  7S66 

.002  777  778 

361 

130  321 

47  015*31 

19.000  0000 

7.120  3071 

.002  770  0S3 

362 

131041 

47  437  928 

19.020  2976 

7.126  9360 

.002  762  431 

363 

131  769 

47s:;jll7 

19.052  ■ 

7.133  4925 

.002  754  821 

364 

132  496 

48  228  511 

19.078  7840 

7.110  0370 

,002  747 

528 

Powers 

and  Roots. 

Number. 

Squares. 

Cubes. 

y  Roots. 

r  iioots. 

Reciprocals. 

365 

133  225 

48  627  125 

19.104  9732 

7.146  5695 

.002  739  726 

366 

133  956 

49  027  896 

19.131  1265 

7.153  0901 

.002  732  240 

367 

134  689 

49  430  863 

19.157  2441 

7.159  5988 

.002  724  796 

368 

135  424 

49  836  032 

19.183  3261 

7.166  0957 

.002  717  391 

369 

136  161 

50  243  409 

19.209  3727 

7.172  5809 

.002  710  027 

370 

136  900 

50  653  000 

19.235  3841 

7.179  0544 

.002  702  703 

371 

137  641 

51  064  811 

19.201  3603 

7.185  5162 

.002  695  418 

372 

138  384 

51  478  848 

19.287  3015 

7.191  9663 

.002  688  172 

373 

139  129 

51  895  117 

19.313  2079 

7.198  4050 

.002  680  965 

374 

139  876 

52  313  624 

19.339  0796 

7.204  8322 

.002  673  797 

375 

140  625 

52  734  375 

19.304  9167 

7.211  2479 

.002  666  667 

376 

141  376 

53  157  376 

19.390  7194 

7.217  6522 

.002  659  574 

377 

142  129 

53  582  633 

19.416  4878 

7.224  0450 

.002  652  520 

378 

142  884 

54  010  152 

19.442  2221 

7.230  4268 

.002  645  503 

379 

143  641 

54  439  939 

19.467  9223 

7.236  7972 

.002  638  521 

380 

144  400 

54  872  000 

19.493  5887 

7.243  1565 

.002  631  579 

381 

145  161 

55  306  341 

19.519  2213 

7.249  5045 

.002  624  672 

382 

145  924 

55  742  968 

19.544  8203 

7.255  8415 

.002  617  801 

383 

146  689 

56  181  887 

19.570  3858 

7.262  1675 

.002  610  966 

384 

147  456 

56  623  104 

19.595  9179 

7.268  4824 

.002  604  167 

385 

148  225 

57  066  625 

19.6214169 

7.274  7864 

.002  597  403 

386 

148  996 

57  512  456 

19.646  8S27 

7.281  0794 

.002  590  674 

387 

149  769 

57  960  603 

19.672  3156 

7.287  3617 

.002  583  979 

388 

150  544 

58  411  072 

19.697  7156 

7.293  6330 

.002  577  320 

389 

151  321 

58  863  869 

19.723  0829 

7.299  8936 

.002  570  694 

390 

152  100 

59  319  000 

19.748  4177 

7.306  1436 

.002  564  103 

391 

152  881 

59  776  471 

19.773  7199 

7.312  3828 

.002  557  545 

392 

153  664 

60  236  288 

19.798  9899 

7.318  6114 

.002  551  020 

,  393 

154  449 

60  698  457 

19.824  2276 

7.324  8295 

.002  544  529 

*  394 

155  236 

61  162  984 

19.849  4332 

7.331  0369 

.002  538  071 

395 

156  025 

61  629  875 

19.874  6069 

7.337  2339 

.002  531  646 

396 

156  816 

62  099  136 

19.899  7487 

7.343  4205 

.002  525  253 

397 

157  609 

62  570  773 

19.924  8588 

7.349  5966 

.002  518  892 

398 

158  404 

63  044  792 

19.949  9373 

7.355  7624 

.002  512  563 

399 

159  201 

63  521 199 

19.974  9844 

7.361  9178 

.002  506  266 

400 

160  000 

64  000  000 

20.000  0000 

7.368  0630 

.002  500  000 

401 

160  801 

64  481  201 

20.024  9844 

7.374  1979 

.002  493  766 

402 

161  604 

64  964  808 

20.049  9377 

7.380  3227 

.002  487  562 

403 

162  409 

65  450  827 

20.074  8599 

7.386  4373 

.002  481  390 

404 

163  216 

65  939  264 

20.099  7512 

7.392  5418 

.002  475  248 

405 

164  025 

66  430  125 

20.124  6118 

7.398  6363 

.002  469  136 

406 

164  836 

66  923  416 

20.149  4417 

7.404  7206 

.002  463  054 

407 

165  649 

67  419  143 

20.174  2410 

7.410  7950 

.002  457  002 

408 

166  464 

67  917  312 

20.199  0099 

7.416  8595 

.002  450  980 

409 

167  281 

68  417  929 

20.223  7484 

7.422  9142 

.002  444  988 

410 

168  100 

68  921  000 

20.248  4567 

7.428  9589 

.002  439  024 

411 

168  921 

69  426  531 

20.273  1349 

7.434  9938 

.002  433  090 

412 

169  744 

69.934  528 

20.297  7831 

7.441  0189 

.002  427  184 

413 

170  569 

70  444  99? 

20.322  4014 

7.447  0343 

.002  421  308 

414 

171  396 

70  957  944 

20.346  9899 

7.453  0399 

.002  415  459 

415 

172  225 

71  473  375 

20.371  5488 

7.459  0359 

.002  409  639 

416 

173  056 

71  991  296 

20.396  0781 

7.465  0223 

.602  406  846 

Powers  and  Roots. 


Number. 

Squares. 

<  'ubes. 

t  l: 

; 

Eta  iprocala. 

417 

173  889 

72  511  713 

20. 12"  577'.' 

7.470  9991 

.002  398  082 

418 

174724 

73  034 (    - 

20.4  15  i 

7.476  9     1 

.002  392:;  11 

419 

17",  561 

73  560  059 

20.469  1895 

7.4829242 

.002  386 

420 

176  400 

710S8  000 

9015 

7.4888724 

.002  380  952 

421 

177.11 

74618461 

20.5182845 

7.4948113 

.002  375  297 

499 

178 

7".  151  448 

20.542  ( 

2     K)7406 

.002  369 

423 

178929 

75  686  S 

20.5661 

7.506  € 

.002  364  066 

424 

179  776 

76225024 

2  1.591 

7.512  5715 

.002  353  491 

425 

180  1 

76562 

20.6155281 

7.51  s  17 

.002  3.52  911 

426 

1S1  476 

77  308  776 

20.02,9  7674 

7.5243652 

.002  347  413 

427 

182  329 

77854  1 

20.663  97S3 

7.530  2482 

.002  341  920 

183  184 

7-  402752 

20.6*3  1609 

7.536  1221 

.002  336  449 

429 

184  041 

7>  953 

20.7123152 

7.541  9S67 

.002  331  002 

430 

1-1  900 

79  507  000 

20.7364414 

7.547  8423 

.002  325  581 

431 

1S5  761 

80  0G2  991 

20.7 

7.553  6SS8 

.002  320  186 

432 

186  624 

-  1  621  563 

20.7846097 

7.559  5263 

.002  311  815 

433 

187  489 

81182  7  1 

20.S08  6520 

7.565  35 ;  - 

.002  309  469 

434 

188  356 

81  746  504 

20.8326667 

7.571  1743 

.002  304  147 

435 

189  225 

82  312  875 

20.856  1 

7.576  9S49 

.002  298  851 

436 

190  096 

82  881856 

20.S80  6130 

7.582  78 

.002  292      - 

437 

190  969 

83  453  453 

20.904  5450 

7.588  5793 

.002  28.8  330 

438 

191  8 1 1 

84  027  672 

20.9284495 

7.594  3633 

.002  283  105 

439 

192  721 

8 1  604  519 

20.952  3268 

7.6001 

.002  277  904 

440 

193  600 

85  184  000 

20.976  1770 

7.605  9049 

.002  272  727- 

441 

194  481 

85  766  121 

21.000  0000 

7.611  6626 

.002  267  574 

442 

195  364 

86  350  888 

21.023  7960 

7.617  4116 

.002  262  443 

443 

196  249 

86  938  307 

21.047  5652 

7.623  1519 

.002  257  336 

444 

197  136 

B7  528  384 

21.071  3075 

7.628  8S37 

.002  252  252 

445 

198  025 

88  121 125 

21.095  0231 

7.634  6067 

.002  247  191 

440 

198  916 

88  716  536 

21.118  7121 

7.640  3213 

.002  242  152 

447 

199  809 

89  314  623 

21.142  3715 

7.646  0272 

.002  237  136 

448 

200  704 

89  915  392 

21.1660105 

7.651  7247 

.002  232  113 

449 

201601 

90  518  849 

21.189  6201 

7.657  4138 

.002  227  171 

450 

202  500 

91  125  000 

21.213  2034 

7.663  0943 

.002  222  222 

451 

203  401 

91  733  851 

21.236  7606 

7.668  7665 

.002217295 

452 

204  304 

92  345  408 

21.260  2916 

7.674  4303 

.002  212  389 

453 

205  209 

92  959  677 

21.283  7967 

7.680  0857 

.002  207  506 

454 

206116 

93  576  664 

21.307  2758 

7.6S5  7323 

.002  202  643 

455 

207  025 

94  196  375 

21.330  7290 

7.691  3717 

.002  197  802 

456 

207  936 

94  813  816 

21.351  1565 

7.697  0023 

.002  192  982 

457 

208  849 

.'5  413  993 

21.377      - 

7.7026246 

.002  188  184 

458 

209  764 

96  071  912 

21.4009346 

7.708  2388 

.002  183  406 

459 

210  681 

96  702  579 

21.4242853 

7.718  S448 

.002  178  649 

460 

211600 

97  336  000 

21.447  6106 

7.719  412.; 

.002  173  913 

461 

212  521 

97  972  181 

21.170  9106 

7.725  0325 

.00-2  169  197 

462 

213  144 

•11128 

21.494  1853 

7.730  6141 

.002  164  502 

;• 

211369 

99  252847 

21.517  4348 

7.7361877 

.002  159  827 

4-.; 

■J  15  2% 

99  897  3 1 1 

21.510- 

7.711  7 

,002  155  172 

465 

210  i 

100  514  625 

21.563  - 

7.747  3109 

.002  150  538 

466 

217  156 

101  194  C96 

21.587  0 

7.752  8606 

.002  1 1" 

218  089 

101 847  { 

21.610  1-   - 

7.758  4023 

.002  141  328 

M8 

219024 

102  503  2  2 

21.6333077 

7.763  9361 

.002  136  752 

530 

Powers 

and  Roots 

Squares. 

Cubes. 

f  Roots. 

Number. 

V  Roots. 

Reciprocals. 

469 

219  961 

103  161  709 

21.656  4078 

7.769  4620 

.002  132  196 

470 

220  900 

103  823  000 

21.679  4834 

7.774  9801 

.002  127  660 

471 

221  841 

104  487  111 

21.702  5344 

7.780  4904 

.002  123  142 

472 

222  784 

105  154  048 

21.725  5610 

7.785  9928 

.002  118  644 

473 

223  729 

105  828  817 

21.748  5632 

7.791  4875 

.002  114  165 

474 

224  676 

106  496  424 

21.771  5411 

7.796  9745 

.002  109  705 

475 

225  625 

107  171  875 

21.794  4947 

7.802  4538 

.002  105  263 

476 

226  576 

107  850 176 

21.817  4242 

7.807  9254 

.002  100  840 

477 

227  529 

108  531  333 

21.840  3297 

7.813  3892 

.002  096  436 

478 

228  484 

109  215  352 

21.863  2111 

7.8-18  8456 

.002  092  050 

479 

229  441 

109  902  239 

21.886  0686 

7.824  2942 

.002  087  683 

480 

230  400 

110  592  000 

21.908  9023 

7.829  7353 

.002  083  333 

481 

231  361 

111  284  641 

21.931  7122 

7.835  1688 

.002  079  002 

482 

232  324 

111  980  168 

21.954  4984 

7.840  5949 

.002  074  689 

483 

233  289 

112  678  587 

21.977  2610 

7.846  0134 

.002  070  393 

484 

234  256 

113  379  904 

22.000  0000 

7.851  4244 

.002  066  116 

485 

235  225 

114  084  125 

22.022  7155 

7.856  8281 

.002  061  856 

486 

236  196 

114  791  256 

22.045  4077 

7.862  2242 

.002  057  613 

487 

237  169 

115  501  303 

22.068  0765 

7.867  6130 

.002  053  388 

488 

238  144 

116  214  272 

22.090  7220 

7.872  9944 

.002  049  180 

489 

239  121 

116  930  169 

22.113  3444 

7.878  3684 

.002  044  990 

490 

240  100 

117  649  000 

22.135  9436 

7.883  7352 

.002  040  816 

491 

241  081 

118  370  771 

22.158  5198 

7.889  0946 

.002  036  660 

492 

242  064 

119  095  488 

22.181  0730 

7.894  4468 

.002  032  520 

493 

243  049 

119  823  157 

22.203  6033 

7.899  7917 

.002  028  398 

494 

244  036 

120  553  784 

22.226  1108 

7.905  1294 

.002  024  291 

495 

245  025 

121  287  375- 

22.248  5955 

7.910  4599 

.002  020  202 

496 

246  016 

122  023  936 

22.271  0575 

7.915  7832 

.002  016  129 

497 

247  009 

122  763  473 

22.293  4968 

7.921  0994 

.002  012  072 

498 

248  004 

123  505  992 

22.315  9136 

7.926  4085 

.002  008  032 

499 

249  001 

124  251  499 

22.338  3079 

7.931  7104 

.002  004  008 

500 

250  000 

125  000  000 

22.360  6798 

7.937  0053 

.002  000  000 

501 

251  001 

125  751  501 

22.383  0293 

7.942  2931 

.001  996  008 

502 

252  004 

126  506  008 

22.405  3565 

7.947  5739 

.001  992  032 

503 

253  009 

127  263  527 

22.427  6615 

7.952  8477 

.001  988  072 

504 

254  016 

128  024  064 

22.449  9443 

7.958  1144 

.001  984  127 

505 

255  025 

128  787  625 

22.472  2051 

7.963  3743 

.001  980  198 

506 

256  036 

129  554  216 

22.494  4438 

7.968  6271 

.001  976  285 

507 

257  049 

130  323  843 

22.516  6605 

7.973  8731 

.001  972  387 

508 

258  064 

131  096  512 

22.538  8553 

7.979  1122 

.001  968  504 

509 

259  081 

131  872  229 

22.561  0283 

7.984  3444 

.001  964  637 

510 

260  100 

132  651  000 

22.583  1796 

7.989  5697 

.001960784 

511 

261 121 

133  432  831 

22.605  3091 

7.994  7883 

.001  956  947 

512 

262  144 

134  217  728 

22.627  4170 

8.000  0000 

.001  953  125 

513 

263  169 

135  005  697 

22.649  5033 

8.005  2049 

.001  949  318 

514 

264  196 

135  796  744 

22.671  5681 

8.010  4032 

.001  945  525 

515 

265  225 

136  590  875 

22.693  6114 

8.015  5946 

.001  941  748 

516 

266  256 

137  388  096 

22.715  6334 

8.020  7794 

.001  937  984 

517 

267  289 

138  188  413 

22.737  6341 

8.025  9574 

.001  934  236 

518 

268  324 

138  991  832 

22.759  6134 

8.031 1287 

.001  930  502 

519 

269  361 

139  798  359 

22.781  5715 

8.036  2935 

.001  926  782 

520 

270  400 

140  608  000 

22.803  5085 

8.041  4515 

.001  923  077 

Powers  and  Roots. 


531 


Number. 

1  Squares. 

521 

271  441 

522 

272  484 

523 

273  529 

524 

274  576 

525 

275  625 

526 

276  676 

527 

277  729 

528 

278784 

529 

279  841 

530 

280  900 

531 

2S1961 

532 

283  024 

533 

284  0S9 

534 

285156 

535 

286  2-25 

536 

287  2% 

537 

288  369 

538 

289  444 

539 

290  521 

540 

291600 

541 

292  681 

542 

293  764 

543 

294  849 

544 

295  936 

545 

297  025 

546 

298116 

547 

299  209 

548 

300  304 

549 

301  401 

550 

302  500 

551 

303  601 

552 

304  704 

553 

305  809 

554 

306  916 

555 

308  025 

556 

309  136 

557 

310  249 

558 

311364 

559 

312  481 

560 

313  600 

561 

314  721 

562 

315  844 

563 

316  969 

564 

318  096 

565 

319  225 

566 

320  356 

567 

321  489 

568 

322  (EM 

569 

761 

570 

yoo 

571 

041 

' 

27 184 

Cubes. 

1  Roots. 

9  Roots. 

Reciprocals. 

141  420  761 

22.8254244 

8.046  6030 

.001  919  386 

142  23f, 

22.847  3193 

8.051  7479 

.001  915  709 

143  055  667 

22.S69  1933 

8.056  8862 

.001  912  046 

143877824 

22.891  0463 

8.062  0180 

.001  908  397 

144  703  125 

22,9128785 

8.067  1432 

.001  904  762 

145  531  576 

22.934  6899 

8.072  2620 

.001  901  141 

146  363  1S3 

22.956  4806 

8.077  3743 

.001  897  533 

147  197  952 

22.978  2506 

8.082  4800 

.001  893  939 

148  035  889 

23.000  0000 

8.087  5794 

.001  890  359 

148  877  001 

23.021  7 

8.092  6723 

.001  886  792 

149  721  291 

23.043  4372 

8.097  7589 

.001  883  239 

150  568  768 

23.0651252 

8.102  8390 

.001  879  699 

151419  4.7 

23.086  7928 

8.107  9128 

.001  876  173 

152  273  304 

23.108  4400 

8.112  9803 

.001  872  659 

153  130  375 

23.130  0670 

8.118  0414 

.001  869  159 

153  990  656 

-  1516733 

8.123  0962 

.001  865  672 

154  854  153 

23.1732605 

8.128  1447 

.001  862  197 

155  720  872 

23.194  8270 

8.133  1870 

.001  858  736 

156  590  819 

23.216  3735 

8.138  2230 

.001  855  288 

157  464  000 

23.237  9001 

8.143  2529 

.001  851  852 

158  340  421 

23.259  4067 

8.148  2765 

.001  848  429 

159220088 

23.280  8935 

8.153  2939 

.001  845  018 

160  103  007 

23.302  3604 

8.158  3051 

.001  841  621 

160  989  184 

23.323  8076 

8.163  3102 

.001  838  235 

161  878  625 

23.345  2351 

8.168  3092 

.001  834  862 

162  771  336 

23.366  6429 

8.173  3020 

.001  831  502 

163  667  323 

23.388  0311 

8.178  2888 

.001  828  L54 

164  566  592 

23.409  3998 

8.183  2695 

.001  824  818 

165  469  149 

23.430  7490 

8.188  2441 

.001  821  494 

166  375  000 

23.452  0788 

8.193  2127 

.001  818  182 

167  284  151 

23.473  3892 

8.198  1753 

.001  814  882 

168  196  608 

23.494  6802 

8.203  1319 

.001  811  594 

169  112  377 

23.515  9520 

8.208  0825 

.001  808  318 

170  031  464 

23.537  2046 

8.213  0271 

.001  805  054 

170  953  875 

23.558  4380 

8.217  9657 

.001  801  802 

171  879  616 

23.579  6522 

8.222  8985 

.001  798  561 

172  808  693 

23.600  8474 

8.227  8254 

.001  795  332 

173  741112 

23.622  0236 

8.232  7463 

.001  792  115 

174  676  879 

23.643  1803 

8.237  6614 

.001  788  909 

175  616  000 

23.664  3191 

8.242  5706 

.001  785  714 

176  558  481 

23.685  4386 

8.247  4740 

.001  782  531 

177  504  328 

23.706  5392 

8.252  3715 

.001  779  359 

178  453  547 

23.727  6210 

8.257  2635 

.001  776  199 

179  406  144 

23.748  6S42 

8.262  1492 

.001  773  050 

SG2  125 

23.769  7286 

8.267  0294 

.001  769  912 

181  321  496 

23.790  7545 

8.271  9039 

.001  766  784 

182  284  263 

23.811  7618 

8.276  7726 

.001  763  668 

183  250  ; 

23.832  7506 

8.281  6255 

.001  760  563 

1  - 1  221 1  009 

23.853  7209 

8.286  4928 

.001  757  469 

185  193  000 

•71  6728 

8.291  34 1 1 

.001  754  386 

186  169411 

.  -95  6063 

8.296  1903 

.001  751  313 

187  149  . 

23.916  5215 

8.301  0304 

.001  748  252 

532 

Powers  and  Roots. 

Number. 

Squares. 

Cubes. 

I  Ruots. 

f  Roots. 

Reciprocals. 

573 

328  329 

188  132  517 

23.937  4184 

8.305  8651 

.001  745  201 

574 

329  476 

189119224 

23.958  2971 

8.310  6941 

.001  742  160 

575 

330  625 

190  109  375 

23.979  1576 

8.315  5175 

.001  739  130 

576 

331  776 

191  102  976 

24.000  0000 

8.320  3353 

.001  736  111 

577 

332  927 

192  100  033 

24.020  8243 

8.325  1475 

.001  733  102 

578 

334  084 

193  100  552 

24.041  6306 

8.329  9542 

.001  730  104 

579 

335  241 

194  104  539 

24.062  4188 

8.334  7553 

.001  727  116 

580 

336  400 

195  112  000 

24.083  1891 

8.339  5509 

.001  724  138 

581 

337  561 

196  122  941 

24.103  9416 

8.344  3410 

.001  721 170 

582 

338  724 

197  137  368 

24.124  6762 

8.349  1256 

.001  718  213 

583 

339  889 

198  155  2S7 

24.145  3929 

8.353  9047 

.001  715  266 

584 

341  056 

199  176  704 

24.166  0919 

8.358  6784 

.001  712  329 

585 

342  225 

200  201  625 

24.186  7732 

8.363  4466 

.001  709  402 

586 

343  396 

201  230  056 

24.207  4369 

8.368  2095 

.001  706  485 

587 

344  569 

202  262  003 

24.228  0829 

8.372  9668 

.001  703  578 

588 

345  744 

203  297  472 

24.248  7113 

8.377  7188 

.001  700  680 

589 

346  921 

204  336  469 

24.269  3222 

8.382  4653 

.001  697  793 

590 

348100 

205  379  000 

24.289  9156 

8.387  2065 

.001  694  915 

591 

349  281 

206  425  071 

24.310  4996 

8.391  9428 

.001  692  047 

592 

350  464 

207  474  688 

24.331  0501 

8.396  6729 

.001  689  189 

593 

351  649 

208  527  857 

24.351  5913 

8.401  3981 

.001  686  341 

594 

352  836 

209  584  584 

24.372  1152 

8.406  1180 

.001  6S3  502 

595 

354  025 

210  644  875 

24.392  6218 

8.410  8326 

.001  680  672 

596 

355  216 

211  708  736 

24.413  1112 

8.415  5419 

.001  677  852 

597 

356  409 

212  776  173 

24.433  5834 

8.420  2460 

.001  675  042 

598 

357  604 

213  847  192 

24.454  0385 

8.424  9448 

.001  672  241 

599 

358  801 

214  921  799 

24.474  4765 

8.429  6383 

.001  669  449 

600 

360  000 

216  000  000 

24.494  8974 

8.434  3267 

.001  666  667 

601 

361  201 

217  0S1  801 

24.515  3013 

8.439  0098 

.001  663  894 

602 

362  404 

218  167  208 

24.535  6883 

8.443  6877 

.001  661  130 

603 

363  609 

219  256  227 

24.556  0583 

8.448  3605 

.001  658  375 

604 

364  816 

220  348  864 

24.576  4115 

8.453  0281 

.001  655  629 

605 

366  025 

221  445  125 

24.596  7478 

8.457  6906 

.001  652  893 

606 

367  236 

222  545  016 

24.617  0673 

8.462  3479 

.001  650  165 

607 

368  449 

223  648  543 

24.637  3700 

8.467  0001 

.001  647  446 

608 

369  664 

224  755  712 

24.657  6560 

8.471  6471 

.001  644  737 

609 

370  881 

225  866  529 

24.677  9254 

8.476  2892 

.001  642  036 

610 

372  100 

226  981  000 

24.698  1781 

8.4S0  9261 

.001  639  344 

611 

373  321 

228  099  131 

24.718  4142 

8.485  5579 

.001  636  661 

612 

374  544 

229  220  928 

24.738  6338 

8.490  1848 

.001  633  987 

613 

375  769 

230  346  397 

24.758  8368 

8.494  8065 

.001  631  321 

614 

376  996 

231  475  544 

24.779  0234 

8.499  4233 

.001  628  664 

615 

378  225 

232  608  375 

24.799  1935 

8.504  0350 

.001  626  016 

616 

379  456 

233  744  896 

24.819  3473 

8.508  6417 

.001  623  377 

617 

380  689 

234  885  113 

24.839  4847 

8.513  2435 

.001  620  746 

618 

381  924 

236  029  032 

24.859  6058 

8.517  8403 

.001  618  123 

619 

383  161 

237  176  659 

24.879  7106 

8.522  4331 

.001  615  509 

620 

384  400 

238  328  000 

24.899  7992  | 

8.527  0189 

.001  612  903 

621 

385  641 

239  483  061 

24.919  8716 

8.531  6009 

.001  610  306 

622 

386  884 

240  641  848 

24  939  9278  j 

8.536  1780 

.001  607  717 

623 

388  129 

241  804  367 

24.959  9679 

8.540  7501 

.001  605  136 

624 

389  376 

242  970  624 

24.979  9920  j 

8.545  3173 

.001  602  564 

Powers 

and  Roots. 

533 

Number. 

Squares 

Cubes. 

/Boots. 

t  Koots. 

Reciprocals. 

625 

390  625 

244140625 

25.000  0000 

8.549  8797 

.001  600  000 

626 

391  876 

245  134  376 

25.019  9920 

8.554  4372 

.001  597  1 1 1 

627 

393  129 

246  491  883 

25.039  9681 

8.558  9899 

.001  594  896 

628 

394  384 

247  673  152 

25.059  9282 

8.563  5377 

.001  592  357 

829 

395  641 

248  858  1-9 

25.079  8721 

8.568  0807 

.001  589  825 

630 

396  900 

250  047  000 

25.099  8008 

8.572  6189 

.001  587  302 

631 

398  161 

251  239  591 

25.1197134 

8.577  1523 

.001  584  786 

632 

399  424 

252  435  968 

25.139  6102 

8.581  6809 

.001  582  278 

633 

400  689 

253  636  137 

25.159  4913 

8.586  2247 

.001  579  779 

634 

401  956 

254  8-10  104 

25.179  3566 

8.590  7238 

.001  577  287 

635 

403  225 

256  047  875 

25.199  2063 

8.595  2380 

.001  574  803 

636 

404  496 

257  259  456 

25.219  0404 

8.599  7476 

.001  572  327 

637 

405  769 

258  474  853 

25.238  8589 

8.604  2525 

.001  569  859 

638 

407  011 

259  694  072 

25.258  6619 

8.608  7526 

.001  567  398 

639 

408  321 

260  917  119 

25.278  4493 

8.613  2480 

.001  564  945 

640 

409  600 

202  144  000 

25.298  2213 

8.617  7388 

.001  562  500 

641 

410  881 

263  374  721 

25.317  9778 

8.622  2248 

.001  560  062 

642 

412  164 

264  609  288 

25.337  7189 

8.626  7063 

.001  557  632 

643 

413  449 

265  847  707 

25.357  4447 

8.631 1830 

.001  555  210 

644 

414  736 

267  089  984 

25.377  1551 

8.635  6551 

.001  552  795 

645 

416  025 

268  336  125 

25.396  8502 

8.640  1226 

.001  550  388 

646 

417  316 

269  5S5  136 

25.416  5302 

8.644  5S55 

.001  547  988 

647 

418  609 

270  840  023 

25.436  1947 

8.649  0437 

.001  545  595 

648 

419  904 

272  097  792 

25.455  8441 

8.653  4974 

.001  543  210 

649 

421  201 

273  359  449 

25.475  47-1 

8.657  9465 

.001  540  832 

650 

422  500 

274  625  000 

25.495  0976 

8.662  3911 

.001  538  462 

651 

423  801 

275  894  451 

25.514  7013 

8.666  8310 

.001  536  098 

652 

425104 

277  167  808 

25.534  2907 

8.671  2665 

.001  533  742 

653 

426  409 

278  445  077 

25.553  8647 

8.675  6974 

.001  531  394 

654 

427  716 

279  726  264 

25.573  42: ;7 

8.680  1237 

.001  529  052 

655 

429  025 

281  Oil  375 

25.592  9678 

8.684  5456 

.001  526  718 

656 

430  336 

282  300  416 

25.612  4969 

8.6S8  9630 

.001  524  390 

657 

431649 

283  593  393 

25.632  0112 

8.693  3759 

.001  522  070 

658 

432  964 

284  890  312 

25.651  5107 

8.697  7843 

.001  519  757 

659 

434  281 

286  191 179 

25.670  9953 

8.702  1882 

.001  517  451 

660 

435  600 

287  496  000 

25.690  4652 

8.706  5877 

.001  515  152 

661 

436  921 

288  804  781 

25.709  9203 

8.710  9827 

.001  512  859 

662 

438  244 

290  117  528 

25.729  3607 

8.715  3734 

.001  510  574 

663 

439  569 

291  434  247 

25.748  7864 

8.719  7596 

.001  508  296 

664 

440  896 

292  754  944 

25.768  1975 

8.724  1414 

.001  506  024 

665 

442  225 

294  079  625 

25.787  5939 

8.728  5187 

.001  503-759 

666 

443  556 

295  408  2% 

25.806  9758 

8.732  8918 

.001  501  502 

667 

444  889 

296  740  963 

25.826  3431 

8.737  2604 

.001  499  2.50 

668 

446  224 

298  077  632 

25.845  6960 

8.741  6246 

.001  497  006 

669 

447  561 

299  418  309 

25.865  0343 

8.745  9846 

.001  494  768 

670 

448  900 

300  763  000 

25.884  3582 

8.750  3401 

.001  492  537 

671 

450  241 

302  111  711 

25.903  6677 

8.754  6913 

.001  490  313 

672 

451584 

303  464  448 

25.922  9628 

8.759  0383 

.001  4S8  095 

673 

452  929 

304  821  217 

25.9422 

8.763  3809 

.001  485  884 

674 

154  276 

306  182  024 

25.961  5100 

8.767  7192 

.001  483  680 

675 

625 

307  546  875 

25.9807621 

8.772  0532 

.001  4S1  481 

676 

156  976 

308  915  77f, 

■J''.. (KJO  0000 

8.776  3830 

.001  179  290 

534 


Powers  and  Roots. 


Number. 

Squares. 

Cubes. 

»' Roots. 

f  Roots. 

Reciprocals. 

677 

458  329 

310  288  733 

26.019  2237 

.  8.780  7084 

.001  477  105 

678 

459  684 

311  665  752 

26.038  4331 

8.785  0296 

.001  474  926 

679 

461  041 

313  046  839 

26.057  6284 

8.789  3466 

.001  472  754 

680 

462  400 

314  432  000 

26.076  8096 

8.793  6593 

.001  470  588 

681 

463  761 

315  821241 

26.095  9767 

8.797  9679 

.001  468  429 

682 

465  124 

317  214  568 

26.115  1297 

8.802  2721 

.001  466  276 

683 

466  489 

318  611  9S7 

26.134  2687 

8.806  5722 

.001  464  129 

684 

467  856 

320  013  504 

26.153  3937 

8.810  8681 

.001  461  988 

685 

469  225 

321  419  125 

26.172  5047 

8.815  1598 

.001  459  854 

686 

470  596 

322  828  856 

26.191  6017 

8.819  4474 

.001  457  726 

687 

471  969 

324  242  703 

26.210  6848 

8.823  7307 

.001  455  604 

688 

473  344 

325  660  672 

26.229  7541 

8.828  0099 

.001  453  488 

689 

474  721 

327  082  769 

26.248  8095 

8.832  2850 

.001  451  379 

690 

476  100 

328  509  000 

26.267  8511 

8.836  5559 

.001  449  275 

691 

477  481 

329  939  371 

26.286  8789 

8.840  8227 

.001  447  178 

692 

478  864 

331  373  888 

26.305  8929 

8.845  0854 

.001  445  087 

693 

480  249 

332  812  557 

26.324  8932 

8.849  3440 

.001  443  001 

694 

481  636 

334  255  384 

26.343  8797 

8.853  5985 

.001  440  922 

695 

483  025 

335  702  375 

26.362  8527 

8.857  8489 

.001  438  849 

696 

484  416 

337  153  536 

26.381  8119 

8.862  0952 

.001  436  782 

697 

485  809 

338  608  873 

26.400  7576 

8.866  3375 

.001  434  720 

698 

487  204 

340  068  392 

26.419  6896 

8.870  5757 

.001  432  665 

699 

488  601 

341  532  099 

26.438  6081 

8.874  8099 

.001  430  615 

700 

490  000 

343  000  000 

26.457  5131 

8.879  0400 

.001  428  571 

701 

491  401 

344  472  101 

26.476  4046 

8.883  2661 

.001  426  534 

702 

492  804 

345  948  408 

26.495  2826 

8.887  4882 

.001  424  501 

703 

494  209 

347  428  927 

26.514  1472 

8.891  7063 

.001  422  475 

704 

495  616 

348  913  664 

26.532  9983 

8.895  9204 

.001  420  455 

705 

497  025 

350  402  625 

26.551  8361 

8.900  1304 

.001  418  440 

706 

498  436 

351  895  816 

26.570  6605 

8.904  3366 

.001  416  431 

707 

499  849 

353  393  243 

26.589  4716 

8.908  5387 

.001  414  427 

708 

501264 

354  894  912 

26.608  2694 

8.912  7369 

.001  412  429 

709 

502  681 

356  400  829 

26.627  0539 

8.916  9311 

.001  410  437 

710 

504  100 

357  911  000 

26.645  8252 

8.921  1214 

.001  408  451 

711 

505  521 

359  425  431 

26.664  5833 

8.925  3078 

.001  406  470 

712 

506  944 

360  944  128 

26.683  3281 

8.929  4902 

.001  404  494 

713 

508  369 

362  467  097 

26.702  0598 

8.933  6687 

.001  402  525 

t  714 

509  796 

363  994  344 

26.720  7784 

8.937  8433 

.001  400  560 

715 

511  225 

365  525  875 

26.739  4839 

8.942  0140 

.001  398  601 

716 

512  656 

367  061  696 

26.758  1763 

8.946  1809 

.001  396  648 

*717 

514  089 

368  601  813 

26.776  8557 

8.950  3438 

.001  394  700 

718 

515  524 

•  370146  232 

26.795  5220 

8.954  5029 

.001  392  753 

719 

516  961 

371  694  959 

26.814  1754 

8.958  6581 

.001  390  821 

720 

518  400 

373  248  000 

26.832  8157 

8.962  8095 

.001  388  889 

721 

519  841 

374  805  361 

26.851  4432 

8.966  9570 

.001  386  963 

722 

521  284 

376  367  048 

26.870  0577 

8.971 1007 

.001  385  042 

723 

522  729 

377  933  067 

26.888  6593 

8.975  2406 

.001  383  126 

724 

524  176 

379  503  424 

26.907  2481 

8.979  3766 

.001  381  215 

725 

525  625 

381  078  125 

26.925  8240 

8.983  5089 

.001  379  310 

726 

527  076 

382  657  17S 

26.944  3872 

8.987  6373 

.001  377  410 

727 

528  529 

384  240  583 

26.962  9375 

8.991  7620 

.001  375  516 

728 

529  984 

3S5  828  352 

26.981 4751 

8.995  8899 

.001  373  626 

Powers  and  Roots. 


535 


Number. 

Squares. 

I'll': 

•  K..otd. 

f  Roots. 

Reciprocals. 

729 

531441 

387  420  489 

27.000  0000 

9.000  0000 

.001  371  7  12 

' 

532900 

■  017  000 

27.0185122 

9.004113.1 

.001  369  863 

731 

534  361 

390  617  891  | 

27.037  0117 

9.CM  -  - 

.001 

3  - 

324 

168 

27.0.V5  4985 

9.012  3288 

.001  366  120 

733 

537    -  1 

393  332  837 

27.0739727 

9.0164     ■ 

.001364  256 

734 

538" 

■  4 16  904 

27.0924344 

9.020  52 

.001  362  398 

735 

540  i 

397  065  375 

27.110  88   1 

9.024  6239 

.001  360  544 

736 

541696 

39> 

27.129: 

9.028  71 19 

.001  358  696 

J  ' 

543  169 

400  315  553 

27.117  7119 

9.032  8021 

.001  356  8o2 

738 

544  644 

401947  272 

27.166  1554 

9.036  8857 

.001  355  014 

739 

546  121 

403  583  419 

27.1-1  I 

9.040  9655 

.001  353  180 

740 

547  600 

221000 

27.202  9140 

9.045  0419 

.001  351 

741 

549  081 

406  869  0-1 

27.221  3152 

9.049  1142 

.001  349  528 

742 

550  56-1 

408  518  188 

27.239  6769 

9.053  1831 

.001  347  709 

74:: 

552  049 

410  172  407 

27.258  0263 

9.057  21-2 

.001  345  895 

744 

553 

411  830784 

27.27-;: 

9.061  3098 

.001  344  086 

74.'. 

555  025 

413  493  625 

27.2946881 

9.065  3' 

.001  342  282 

746 

556  516 

415  160  i 

27.313  0006 

9.069  1220 

.001  340  483 

747 

558  009 

416  83272 

27.331  3007 

9.073  4726 

.001338  688 

748 

559  504 

41S508  992 

27.349  5887 

9.077  5197 

.001  336  898 

561001 

420  189  749 

-7. 

9.081  5631 

.001  335  113 

750 

562  500 

421  875  000 

27.3861279 

9.085  6030 

.001  333  333 

751 

564  001 

423  564  751 

27.404  3792 

9.089  6352 

.001  331  558 

752 

565  504 

425  239  008 

27.4226184 

9.093  6719 

.001  329  787 

753 

567  009 

426  957  777 

27.4408 

9.097  7010 

.001  328  021 

754 

568  516 

-  661064 

27.459  0604 

9.101  72 

.001  326  260 

755 

570  025 

430  368>7". 

27.477  2633 

9.105  7485 

.001  324  503 

756 

571536 

432  0-1  216 

27.495  4542 

9.109  7669 

.001  322  751 

757 

573  049 

4:;:;  7. 16  093 

27.513  6330 

9.113  7818 

.001  321  004 

758 

574  564 

4:;-.  519  512 

27.531  7998 

9.117  7931 

.001  319  261 

759 

576  081 

437  21.')  479 

27.5499546 

9.121  8010 

.001  317  523 

760 

577  600 

438  976  000 

27.568  0975 

9.125  8053 

.001  315  789 

761 

579  121 

440  711U-1 

27.586  2284 

9.129  8061 

.001  314  060 

762 

580  644 

442  450  728 

27.604  3475 

9.133  8034 

.001  312  336 

763 

-  J  169 

444  194  947 

27.6224546 

9.137  7971 

.001  310  616 

764 

583  696 

445  943  711 

27.640  5499 

9.141  7-71 

.001  308  901 

765 

585-- 

447  697  125 

27.658  6334 

9.145  7742 

.001  307  190 

766 

586  756 

449  4.35  096 

27.676  7050 

9.149  7576 

.001  305  483 

:--_-.' 

451  217  663 

27.694  ' 

9.153  7375 

.001  303  7S1 

• 

589-.; 

452  984  £   - 

27.712  8129 

9.157  7139 

.001  302  083 

591361 

454  756  609 

27.730  8492 

9.1616869 

.001  300  390 

770 

2  900 

000 

27.748  - 

9.165  6565 

.001  298  701 

771 

594  441 

458  314  Oil 

27.766  8868 

9.169  6225 

.001  297  017 

595  96  t 

'099  648 

27.784  8880 

9.173."- 

.001  295  337 

773 

597    - 

461  889  917 

27.8028775 

9.177  5145 

.001  293  661 

771 

599  076 

1  824 

27.820  - 

9.1S1  5003 

.001  291  990 

77"' 

465484  375 

27.8388218 

9.185  4.727 

.001  290  323 

77-3 

602  17.; 

~  288  576 

27.8567766 

9.1*9  4018 

.001288  660 

777 

603  7- 1 

27.-717197 

9.193  3474 

.001  2S7  001 

77- 

605 

470  910 

27.8926514 

9.1      -•   1 

.001  285  347 

779 

606  841 

172 

27.910  5715 

9.201  2286 

.001  283  697 

780 

608 

!71  .V.2  000 

27.928  4801 

9.205  1641 

.001  282  051 

530 

Powers 

and  Roots 

Squares. 

Cubes. 

l  Roots. 

Number. 

f  Roots. 

Reciprocals. 

781 

009  961 

476  379  541 

27.946  3772 

9.209  0962 

.001  280  410 

782 

611  524 

478  211  768 

27.964  2629 

9.213  0250 

.001  278  772 

783 

613  089 

480  048  687 

27.982  1372 

9.216  9505 

.001  277  139 

784 

614  656 

481  890  304 

28.000  0000 

9.220  8726 

.001  275  510 

785 

616  225 

483  736  625 

28.017  8515 

9.224  7914 

.001  273  885 

786 

617  796 

485  587  656 

28.035  6915 

9.228  7068 

.001  272  265 

787. 

619  369 

487  443  403 

28.053  5203 

9.232  6189 

.001  270  648 

788 

620  944 

489  303  872 

28.071  3377 

9.236  5277 

.001  269  036 

789 

622  521 

491  169  069 

28.089  1438 

9.240  4333 

.001  267  427 

790 

624  100 

493  039  000 

28.106  9386 

9.244  3355 

.001  265  823 

791 

625  681 

494  913  671 

28.124  7222 

9.248  2344 

.001  264  223 

792 

627  264 

496  793  088 

28.142  4946 

9.252  1300 

.001  262  626 

793 

628  849 

498  677  257 

28.160  2557 

9.256  0224 

.001  261  034 

794 

630  436 

500  566  184 

28.178  0056 

9.259  9114 

.001  259  446 

795 

632  025 

502  459  875 

28.195  7444 

9.263  7973 

.001  257  862 

796 

633  616 

504  358  336 

28.213  4720 

9.267  6798 

.001  256  281 

797 

635  209 

506  261  573 

28.231 1884 

9.271  5592 

.001  254  705 

798 

636  804 

508  169  592 

28.248  8938 

9.275  4352 

.001  253  133 

799 

638  401 

510  082  399 

28.266  5881 

9.279  3081 

.001  251  564 

800 

640  000 

512  000  000 

28.284  2712 

9.283  1777 

.001  250  000 

801 

641601 

513  922  401 

28.301  9434 

9.287  0444 

.001  248  439 

802 

643  204 

515  849  608 

28.319  6045 

9.290  9072 

.001  246  883 

803 

644  809 

517  781  627 

28.337  2546 

9.294  7671 

.001  245  330 

804 

646  416 

519  718  464 

28.354  8938 

9.298  6239 

.001  243  781 

805 

648  025 

521  660  125 

28.372  5219 

9.302  4775 

.001  242  236 

806 

649  636 

523  606  616 

28.390  1391 

9.306  3278 

.001  240  695 

807 

651  249 

525  557  943 

28.407  7454 

9.310  1750 

.001  239  157 

808 

652  864 

527  514  112 

28.425  3408 

9.314  0190 

.001  237  624 

809 

654  481 

529  475  129 

28.442  9253 

9.317  8599 

.001  236  094 

810 

656  100 

531  441  000 

28.460  4989 

9.321  6975 

.001  234  568 

811 

657  721 

533  411  731 

28.478  0617 

9.325  5320 

.001  233  046 

812 

659  344 

535  387  328 

28.495  6137 

9.329  3634 

.001  231  527 

813 

660  969 

537  367  797 

28.513  1549 

9.333  1916 

.001  230  012 

814 

662  596 

539  353  144 

28.530  6852 

9.337  0167 

.001  228  501 

815 

664  225 

541  343  375 

28.548  2048 

9.340  8386 

.001  226  994 

816 

665  856 

543  338  496 

28.565  7137 

9.344  6575 

.001  225  499 

817 

667  489 

545  338  513 

28.583  2119 

9.348  4731 

.001  223  990 

818 

669  124 

547  343  432 

28.600  6993 

9.352  2857 

.001  222  494 

819 

670  761 

549  353  259 

28.618  1760 

9.356  0952 

.001  221  001 

820 

672  400 

551  368  000 

28.635  6421 

9.359  9016 

.001  219  512 

821 

674  041 

553  387  661 

28.653  0976 

9.363  7049 

.001  218  027 

822 

675  684 

555  412  248 

28.670  5424 

9.367  5051 

.001  216  545 

823 

677  329 

557  441  767 

28.687  9716 

9.371  3022 

.001  215  067 

824 

678  976 

559  476  224 

28.705  4002 

9.375  0963 

.001  213  592 

825 

680  625 

561  515  625 

28.722  8132 

9.378  8873 

.001  212  121 

826 

682  276 

563  559  976 

28.740  2157 

9.382  6752 

.001  210  654 

827 

683  929 

565  609  283 

28.757  6077 

9.386  4600 

.001  209  190 

828 

685  584 

567  663  552 

28.774  9891 

9.390  2419 

.001  207  729 

829 

687  241 

569  722  789 

28.792  3601 

9.394  0206 

.001  206  273 

830 

688  900 

571  787  000 

28.809  7206 

9.397  7964 

.001  204  819 

831 

690  561 

573  856  191 

28.827  0706 

9.401  5691 

.001  203  369 

832 

692  224 

575  930  368 

28.844  4102 

9.405  3387 

.001  201  923 

Powers 

and  Roots 

037 

Squares. 

Cubes. 

Number. 

1  Roots. 

I  Boots, 

Reciprocals. 

833 

693  889 

578  009  537 

28.861  7394 

9.409  L054 

.001  200  480 

834 

695  556 

580  093  704 

28.8790582 

9.412  8690 

.001  199  041 

835 

697  225 

582  1 82  875 

28.8%  \\t\M 

9.416  6297 

.001  197  605 

836 

698  896 

584  277  056 

28.913  6646 

9.420  3873 

.001196  172 

887 

700  569 

586  376  2".:; 

28.930  9523 

9.424  1420 

.001  194  743 

.*:> 

702  244 

588  480  472 

28.948  2297 

9. 127  8936 

.001  193  317 

839 

703  921 

590  5S9  719 

28.965  4967 

9.431  6423 

.001 191  895 

8-10 

705  600 

592  704  000 

28.982  7535 

9.435  3800 

.001 190  476 

841 

707  2S1 

59 1  823  321 

29.000  0000 

9.439  1307 

.001  189  061 

842 

708  964 

596  947  688 

29.017  2363 

9.442  8704 

.001  187  648 

843 

710  649 

599  077  107 

29.0:'  I  1623 

9.446  6072 

.001  186  240 

844 

712  336 

601  211584 

29.051  6781 

9.450  3410 

.001  184  834 

845 

714  025 

603  351 125 

29.068  8837 

9.454  0719 

.001 183  432 

846 

715  716 

605  495  736 

29.086  0791 

9.457  7999 

.001  182  033 

847 

717  409 

607615423 

29.103  2644 

9.461  5249 

.001  180  638 

848 

719  104 

609  800  192 

29.120  4396 

9.465  2470 

.001 179  245 

849 

720  801 

611960  049 

29.137  6046 

9.468  9661 

.001 177  856 

850 

722  500 

614  125  000 

29.154  7595 

9.472  6824 

.001  176  471 

851 

721201 

616  295  051 

29.171  9043 

9.476  3957 

.001  175  088 

852 

725  904 

618470  208 

29.1S9  0390 

9.480  1061 

.001 173  709 

853 

727  609 

620  6.50  477 

29.206  1637 

9.483  8136 

.001  172  333 

854 

729  316 

622835  864 

29.223  2784 

9.487  5182 

.001  170  960 

855 

731  025 

625  026  375 

29.240  3830 

9.491  2200 

.001  169  591 

856 

732  736 

627  222  016 

29.257  4777 

9.494  9188 

.001 168  224 

857 

734  449 

629  422  793 

29.274  5623 

9.498  6147 

.001 166  861 

>- 

736  164 

631  628  712 

29.291  6370 

9.502  3078 

.001  165  501 

859 

737  881 

633  839  779 

29.308  7018 

9.505  9980 

.001  164  144 

860 

739  600 

636  056  000 

29.325  7566 

9.509  6854 

.001162  791 

861 

741  321 

638  277  381 

29.342  8015 

9.513  3699 

.001  161  440 

862 

743  044 

640  503  928 

29.359  8365 

9.517  0515 

.001  160  093 

863 

74 1  769 

642735647 

29.376  8616 

9.520  7303 

.001 158  749 

864 

746  496 

644  972  544 

29.393  8769 

9.5244063 

.001  157  407 

865 

748  225 

647  214  625 

29.410  8823 

9.528  0794 

.001  1.56  069 

866 

749  956 

649  461  896 

29.4278779 

9.531  7497 

.001  1.54  734 

867 

751  689 

651711363 

29.414  86:17 

9.535  4172 

.001 153  403 

868 

753  424 

653  972  032 

29.461  8397 

9.539  0818 

.001  152  074 

869 

755  161 

656  234  909 

29.478  8059 

9.542  7437 

.001 1.50  748 

870 

756  900 

658  503  000 

29.4957624 

9.546  4027 

.001 149  425 

871 

758  641 

660  776  311 

29.512  7091 

9.550  0589 

.001  148  106 

872 

760  384 

663  054  848 

29.529  6461 

9.553  7123 

.001  146  789 

873 

762  129 

665  338  617 

29.546  5734 

9.557  3630 

.001145  475 

874 

763  876 

667  627  624 

29.563  4910 

9.561  0108 

.001  144  165 

875 

765  625 

669  921  875 

29.580  3989 

9.564  6559 

.001142  857 

876 

767  376 

672  221  376 

29.597  2972 

9.568  2782 

.001  141  553 

877 

769  129 

674  526133 

29.614  1858 

9.571  9377 

.001  140  251 

878 

770  884 

676  836  152 

29.631  0648 

9.575  5745 

.001 138  952 

879 

77264] 

679151439 

29.647  9342 

9.579  2085 

.001  137  656 

*>., 

771400 

681  172  000 

29.664  7939 

9-582  8397 

.001  136  364 

881 

776  161 

683  797  841 

29.6816112 

9.586  4682 

.001  135  074 

882 

777  924 

Csf,  1J8  96S 

29.698  4848 

9.590  0937 

.001 133  787 

883 

77'J  689 

6S8  465:>7 

29.715  3159 

9.593  7169 

.001 132  503 

!"1 

781456 

690  807  104 

29.7: 12  1375 

9.597  3373 

.001  131  222 

538 


Powers  and  Roots. 


Number. 

Squares. 

Cubes. 

1  Roots. 

f  Roots. 

Reciprocals. 

885 

783  225 

693  154  125 

29.748  9496 

9.600  9548 

.001 129  944 

886 

784  996 

695  506  456 

29.765  7521 

9.604  5696 

.001  128  668 

887 

786  769 

697  864  103 

29.782  5452 

9.608  1817 

.001 127  396 

888 

788  544 

700  227  072 

29.799  3289 

9.6117911 

.001  126  126 

889 

790  321 

702  595  369 

29.816  1030 

9.615  3977 

.001 124  859 

890 

792  100 

704  9G9  000 

29.832  8678 

9.619  0017 

.001  123  596 

891 

793  881 

707  347  971 

29.849  6231 

9.622  6030 

.001  122  334 

892 

795  664 

707  932  288 

29.866  3690 

9.626  2016 

.001 121  076 

893 

797  449 

712  121  957 

29.883  1056 

9.629  7975 

.001  119  821 

894 

799  236 

714  516  984 

29.899  8328 

9.633  3907 

.001 118  568 

895 

801  025 

716  917  375 

29.916  5506 

9.636  9812 

.001  117  818 

896 

802  816 

719  323  136 

29.933  2591 

9.640  5690 

.001  116  071 

897 

804  609 

721  734  273 

29.949  9583 

9.644  1542 

.001 114  827 

898 

806  404 

724  150  792 

29.966  6481 

9.647  7367 

.001 113  586 

899 

808  201 

726  572  699 

29.983  3287 

9.651  3166 

.001  112  347 

900 

810  000 

729  000  000 

30.000  0000 

9.654  8938 

.001  111  111 

901 

811  801 

731  432  701 

30.016  6621 

9.658  4684 

.001 109  878 

902 

813  604 

733  870  808 

30.033  3148 

9.662  0403 

.001  108  647 

903 

815  409 

736  314  327 

30.049  9584 

9.665  6096 

.001  107  420 

904 

817  216 

738  763  264 

30.066  5928 

9.669  1762 

.001 106  195 

905 

819  025 

741  217  625 

30.083  2179 

9.672  7403 

.001  104  972 

906 

820  836 

743  677  416 

30.099  8339 

9.676  3017 

.001  103  753 

907 

822  649 

746  142  643 

30.116  4407 

9.679  8604 

.001 102  536 

908 

824  464 

748  613  312 

30.133  0383 

9.6S3  4166 

.001 101  322 

909 

826  281 

751  089  429 

30.149  6269 

9.686  9701 

.001 100  110 

910 

828  100 

753  571  000 

30.166  2063 

9.690  5211 

.001  098  901 

911 

829  921 

756  058  031 

30.182  7765 

9.694  0694 

.001  097  695 

912 

831  744 

758  550  828 

30.199  3377 

9.697  6151 

.001  096  491 

913 

833  569 

761  048  497 

30.215  8899 

9.701 1583 

.001  095  290 

914 

835  396 

763  551  944 

30.232  4329 

9.704  6989 

.001  094  092 

915 

837  225 

766  060  875 

30.248  9669 

9.708  2369 

.001  092  896 

916 

839  056 

768  575  296 

30.265  4919 

9.711  7723 

.001  091  703 

917 

840  889 

771  095  213 

30.282  0079 

9.715  3051 

.001  090  513 

918 

842  724 

773  620  632 

30.298  5148 

9.718  8354 

.001  089  325 

919 

844  561 

776  151  559 

30.315  0128 

9.722  3631 

.001  088  139 

920 

846  400 

778  688  000 

30.331  5018 

9.725  8883 

.001  086  957 

921 

848  241 

781  229  961 

30.347  9818 

9.729  4109 

.001  085  776 

922 

850  084 

783  777  448 

30.3014529 

9.732  9309 

.001  084  599 

923 

851  929 

786  330  467 

30.380  9151 

9.736  4484 

.001  083  423 

924 

853  776 

788  889  024 

30.397  3683 

9.739  9634 

.001  082  251 

925 

855  625 

791  453  125 

30.413  8127 

9.743  4758 

.001  081  081 

926 

857  476 

794  022  776 

30.430  2481 

9.746  9857 

.001  079  914 

927 

859  329 

796  597  983 

30.446  6747 

9.750  4930 

.001  078  749 

928 

861  184 

799  178  752 

30.463  0924 

9.753  9979 

.001  077  586 

929 

863  041 

801  765  089 

30.479  5013 

9.757  5002 

.001  076  426 

930 

864  900 

804  357  000 

30.495  9011 

9.761  0001 

.001  075  269 

931 

866  761 

806  954  491 

30.512  2926 

9.764  4974 

.001  074  114 

932 

868  624 

809  5.57  568 

30.528  6750 

9.767  9922 

.001  072  961 

933 

870  489 

812  166  237 

30.545  0487 

9.771  4845 

.001  071  811 

934 

872  356 

814  7S0  504 

30.561  4136 

9.774  9743 

.001  070  664 

935 

874  225 

S17  400  375 

30.577  7697 

9.778  4616 

.001  069  519 

936 

876  096 

820  025  856 

30.594  1171 

9.781  9466 

.001  068  376 

Powers 

and  Roots 

539 

Squares. 

Cui  •  - 

1  i; 

Number. 

f  R0..1-. 

!;•  ciprocals. 

937 

877  969 

822  656  «).-,:; 

30.610.4557 

'.'.7-5.1288 

.001067  236 

879  8 1 1 

325  293672 

30.ro;  7857 

9.7s-  » 

.001  066  098 

939 

8S1  721 

827  936019 

30.643  1069 

9.792  3861 

.001  (W.J  963 

940 

883  600 

830584  000 

30.659  4194 

9.7958611 

.001063830 

941 

--  i  181 

833  237  621 

30.6757233 

9.799  3336 

.001062699 

942 

887  864 

.  896  888 

30.692  0185 

9.8028036 

.001  061  571 

943 

889249 

-  561  807 

30.708  3051 

9.806  2711 

.001  060  1 15 

944 

891  136 

841  232384 

30.724  5830 

9.809  7362 

.001059  322 

945 

893  025 

843  908  625 

30.7408523 

9.813  1 98  ■ 

.001  058  201 

946 

894  916 

846  590  536 

30.7571130 

9.816  6591 

.001  057  082 

947 

896  809 

849  278  123 

30.773  3651 

9.820  1169 

.001  055  966 

948 

898  704 

851  971  392 

30.789  6086 

9.82::  5723 

.001  05 1  852 

949 

900  601 

854  670349 

30.805  8436 

9.827  0252 

.001053  711 

950 

902  500 

857  375  000 

30.822  0700 

9.830  4757 

.001  052  632 

951 

904  401 

860  085  351 

30.838  2879 

9.833  9238 

.001  051  525 

962 

906  304 

s<'.2  801  408 

30.854  4972 

9.837  3695 

.001  050  420 

953 

908  209 

865  523  177 

30.870  6981 

9.840  8127 

.001  049  31 S 

954 

910  116 

868  250  664 

30.886  8904 

9.844  2536 

.001  048  218 

955 

912  025 

870  983  875 

30.903  07  1  1 

9.847  6920 

.001  047  120 

956 

913  936 

873  722  816 

30.919  2177 

9.851  1280 

.001  046  025 

957 

915  849 

876  467  493 

30.935  4166 

9.854  5617 

.001  044  932 

958 

917  764 

879  217  912 

30.951  5751 

9.857  9929 

.001  043  841 

959 

919  681 

881  974  079 

30.967  7251 

9.861  4218 

.001  042  753 

960 

921  600 

884  736  000 

30.983  8668 

9.864  8483 

.001  041  667 

961 

923  521 

887  503  681 

31.000  0000 

9.868  2724 

.001  040  583 

962 

925  444 

890  277  128 

31.0161248 

9.871  6911 

.001  039  501 

963 

927  369 

893  056  347 

31.032  2113 

9.875  1135 

.001  038  422 

964 

929  296 

895841344 

31.048  3494 

9.878  5305 

.001  037  344 

965 

931225 

898  632  125 

31.064  4491 

9.881  9151 

.001  036  269 

966 

933  156 

901  428  696 

31.080  51H5 

9.885  357 1 

.001  035  197 

967 

935  089 

904  231  063 

31.096  62 

9.888  7673 

.001  034  126 

968 

937  024 

907  039  232 

31.112  6984 

9.8921749 

.001  033  058 

969 

938  961 

909  853  209 

31.128  7648 

9.895  5801 

.001  031  992 

'.'7" 

940  900 

912  673  000 

31.111  8230 

9.898  9830 

.001  030  928 

971 

912  841 

915  498  611 

31.160  8729 

9.902  3835 

.001  029  866 

972 

944  784 

918  330  048 

31.176  91 15 

9.905  7817 

.001  028  807 

973 

946  729 

921  167  317 

31.192  9479 

9.909  1776 

.001027  719 

971 

948  676 

924  010  424 

31.208  97:  ;i 

9.912  5712 

.001  026  694 

975 

9-50  625 

926  859  375 

31.224  9900 

9.915  9624 

.00102-5  641 

976 

952  576 

929  714  176 

31.240  9987 

9.919  3513 

.001  024  590 

977 

954  529 

932574833 

31.256  9992 

9.922  7379 

.001  023  541 

956  484 

935441352 

31.272  9915 

9.926  1222 

.001  022  495 

979 

958  411 

-  u;739 

31.288  97:.7 

9.9295042 

.001  021  450 

980 

960  400 

941  192  000 

31.304  9517 

9.932  8839 

.001020  108 

981 

962  361 

911076  141 

31.320  9195 

9.936  2613 

.001019  168 

982 

964  324 

946  966  168 

31.336  8792 

9.939  6363 

.001  01> 

983 

966  289 

949  862  087 

31.352  8308 

9.943  0092 

.001  017  2   1 

984 

- 

952  763  904 

31.368  77 13 

9.946  3797 

.001  016  260 

985 

970 

955  671  625 

31.384  7097 

9.949  7479 

.001  015  228 

986 

972  196 

958  585  256 

31.400  6 

9.953  1138 

.001  014  199 

987 

971 

961  504  803 

31.4165561 

9.956  4775 

.001  013  171 

988 

976  1  H 

^1430  272 

31.432  4673 

9.959  8389 

.001  012  1 16 

540 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

989 

978  121 

967  361  669 

31.448  3704 

9.963  1981 

.001  011 122 

990 

980  100 

970  299  000 

31.464  2654 

9.966  5549 

.001  010  101 

991 

982  081 

973  242  271 

31.480  1525 

9.969  9055 

.001  009  082 

992 

984  064 

976  191  488 

31.496  0315 

9.973  2619 

.001  008  065 

993 

986  049 

979  146  657 

31.511  9025 

9.976  6120 

.001  007  049 

994 

988  036 

982  107  784 

31.527  7655 

9.979  9599 

.001  006  036 

995 

990  025 

985  074  875 

31.543  6206 

9.983  3055 

.001  005  025 

9% 

992  016 

988  047  936 

31.559  4677 

9.986  6488 

.001  004  016 

997 

994  009 

991  026  973 

31.575  3068 

9.989  9900 

.001  003  009 

998 

996  004 

994  Oil  992 

31.591  1380 

9.993  3289 

.001  002  004 

999 

998  001 

997  002  999 

31.606  9613 

9.996  6656 

.001  001  001 

1000 

1  000  000 

1  000  000  000 

31.622  7766 

10.000  0000 

.001  000  000 

1001 

1  002  001 

1  003  003  001 

31.638  5840 

10.003  3222 

.000  999  0010 

1002 

1  004  004 

1  006  012  008 

31.654  3866 

10.006  6622 

.000  998  0040 

1003 

1  006  009 

1  009  027  027 

31.670  1752 

10.009  9899 

.000  997  0090 

1004 

1  008  016 

1  012  048  064 

31.685  9590 

10.013  3155 

.000  996  0159 

1005 

1  010  025 

1  015  075  125 

31.701  7349 

10.016  6389 

.000  995  0249 

1006 

1  012  036 

1  018  108  216 

31.717  5030 

10.019  9601 

.000  994  0358 

1007 

1  014  049 

1  021 147  343 

31.733  2633 

10.023  2791 

.000  993  0487 

1008 

1  016  064 

1  024  192  512 

31.749  0157 

10.026  5958 

.000  992  0635 

1009 

1  018  081 

1  027  243  729 

31.764  7603 

10.029  9104 

.000  991  0803 

1010 

1  020  100 

1  030  301  000 

31.780  4972 

10.033  2228 

.000  990  0990 

1011 

1  022  121 

1  033  364  331 

31.796  2262 

10.036  5330 

.000  989  1197 

1012 

1  024  144 

1  036  433  728 

31.811  9474 

10.039  8410 

.000  988  1423 

1013 

1  026  169 

1  039  509  197 

31.827  6609 

10.043  1469 

.000  987  1668 

1014 

1  028  196 

1  042  590  744 

31.843  3666 

10.046  4506 

.000  986  1933 

1015 

1  030  225 

1  045  678  375 

31.859  0646 

10.049  7521 

.000  985  2217 

1016 

1  032  256 

1  048  772  096 

31.874  7549 

10.053  0514 

.000  984  2520 

1017 

1  034  289 

1  051  871  913 

31.890  4374 

10.056  3485 

.000  983  2842 

1018 

1  036  324 

1  054  977  832 

31.906  1123 

10.059  6435 

.000  982  3183 

1019 

1  038  361 

1  058  089  859 

31.921  7794 

10.062  9364 

.000  981  3543 

1020 

1  040  400 

1  061  208  000 

31.937  4388 

10.066  2271 

.000  980  3922 

1021 

1  042  441 

1  064  332  261 

31.953  0906 

10.069  5156 

.000  979  4319 

1022 

1  044  484 

1  067  462  648 

31.968  7347 

10.072  8020 

.000  978  4736 

1023 

1  046  529 

1  070  599  167 

31.984  3712 

10.076  0863 

.000  977  5171 

1024 

1  048  576 

1  073  741  824 

32.000  0000 

10.079  3684 

.000  976  5625 

1025 

1  050  625 

1  076  890  625 

32.015  6212 

10.082  6484 

.000  975  6098 

1026 

1  052  676 

1  0S0  045  576 

32.031  2348 

10.085  9262 

.000  974  6589 

1027 

1  054  729 

1  083  206  683 

32.046  8407 

10.089  2019 

.000  973  7098 

1028 

1  056  784 

1  086  373  952 

32.062  4391 

10.092  4755 

.000  972  7626 

1029 

1  058  841 

1  089  547  389 

32.078  0298 

10.095  7469 

.000  971  8173 

1030 

1  060  900 

1  092  727  000 

32.093  6131 

10.099  0163 

.000  970  8738 

1031 

1  062  961 

1  095  912  791 

32.109  1887 

10.102  2835 

.000  969  9321 

1032 

1  065  024 

1  099  104  768 

32.124  7568 

10.105  5487 

.000  968  9922 

1033 

1  067  089 

1 102  302  937 

32.140  3173 

10.108  8117 

.000  968  0542 

1034 

1  069  156 

1 105  507  304 

32.155  8704 

10.112  0726 

.000  967  1180 

1035 

1  071  225 

1  108  717  875 

32.171  4159 

10.115  3314 

.000  966  1836 

1036 

1  073  296 

1  111  934  656 

32.186  9539 

10.118  5882 

.000  965  2510 

1037 

1  075  369 

1 115  157  653 

32.202  4844 

10.121  8428 

.000  964  3202 

1038 

1  077  444 

1 118  386  872 

32.218  0074 

10.125  0953 

.000  963  3911 

1039 

1  079  521 

1  121  622  319 

32.233  5229 

10.128  3457 

.000  962  4639 

1040 

1  081  600 

1  124  864  000 

32.249  0310 

10.131  5941 

.000  961  5385 

Powers  and  Roots. 


541 


Number. 

Bqnarea 

i  'u' 

Mt 

r  B 

Reciprocals. 

1011 

1083  681 

1  128  111  9-21 

32.264.5316 

10.134  8403 

.000  960  61 18 

1042 

1085  7''.! 

1  l:',1366  0S8 

:  _  2800248 

10.1380845 

.000 

1043 

1  087  849 

1  13 1 

2  2       105 

10.111  3266 

.000  958  7728 

1044 

1  089  936 

1  137  893  184 

32.310  9888 

10.144  5667 

.000  957  B544 

1045 

1092 

1  141  166  125 

32  . 

10.147  8047 

.000  9.5(3 

1046 

1094  116 

1144445 

32341  92 

10.151  0406 

.000  956  0229 

1047 

1  0962  19 

1147 

.57  3794 

10.1542744 

.000  955  1098 

104$ 

1098  304 

1  151 

728281 

10.157  5062 

.000  954  1985 

1049 

1100  4"1 

1154  320649 

32.3882695  | 

10.160  7 

.000  953  2888 

1  102  500 

1  157  625  000 

32.403  7 

10.163  9636 

.000  9523810 

1051 

1  104  601 

1  160  935  651 

119  1301 

10.167  1893 

.000  951  4748 

1052 

1  106  704 

1  164  252608 

32,434  5495 

10.170  41-29 

.000  9.50  5703 

1053 

1108  809 

1  ir>7 

32.449  9615 

10.173  ' 

.000  940 

1054 

1  110  916 

1  170  905  464 

32.465  3662 

10.176  8539 

.000  948  7666 

1055 

1  113  025 

1174  211  375 

32,480  7635 

10.180  0714 

.000  947  8673 

10-56 

1  115  136 

1  177  583  616 

32.4961536 

10.183  2868 

.000  946  9697 

1057 

1  117  2}'.! 

1  180  932  193 

2.511  5364 

10.186  5002 

.000  946  0738 

1058 

1  119  364 

1184  287112 

32.526  9119 

10.189  7116 

.000  945  1796 

1059 

1  121  481 

1  187  648  379 

32.5422802 

10.192  9209 

.000  011  2871 

1060 

1  123  600 

1  191  016  000 

32.557  6412 

10.1%  1283 

.000  943  3962 

1061 

1  125  721 

1  194  389  981 

32.572  9949 

10.199  3336 

.000  942  5071 

1062 

1  127  844 

1197  770  328 

:  2.588  3415 

10.202  5369 

.000  941  6196 

1063 

1  129  969 

1  201  157  047 

32.603  5S07 

10.205  7382 

.000  940  "     - 

1064 

1  132  096 

1  204  550  144 

32.619  0129 

10.208  9375 

.000  939  8496 

1065 

1  134  225 

1  207  949  625 

32.634  3377 

10.212  1347 

.000  938  9671 

1066 

1136  356 

1  211  355  496 

32.649< 

10.215  3300 

.000  938  0863 

1067 

1  138  489 

1  214  767  763 

32.664 

10.218  5233 

.000  937  2071 

I06g 

1  140  624 

1  218  1>6  432 

32.680  2693 

10.221  7146 

.000  936  3296 

1069 

1  142  761 

1  221  611  509 

32.695  5654 

10.224  9039 

.000  9:35  4537 

1070 

1  144  900 

1  225  043  000 

32.7108544 

10.228  0912 

.000  934  5794 

1071 

1  147  041 

1  228  480  911 

32.726  1363 

10.231  2766 

.000  933  7068 

1072 

111 

1  231925248 

32.741  4111 

10.234  4599 

.000  932  8358 

1073 

1  151  329 

1  235  376  017 

32.756  6787 

10.237  6413 

.000  931  9664 

1074 

1  153  476 

1  23883 

32.771  9392 

10.240  8207 

.000  931  0987 

1075 

1  155  625 

1  242  296  875 

32.787  1926 

10.243  9981 

.000  930  2326 

1076 

1  157  776 

1  245  766  976 

:-- 

10.247  1735 

.000  9-29  3680 

1077 

1  159  929 

1  249  243  533 

32.817  6782 

10.2.50  3170 

.000  928  5051 

1078 

1  162  084 

1  252  726  552 

32.832  9103 

10.253  5186 

.000  927  6438 

1079 

1164  211 

1256  216  039 

32.848  1354 

10.256  6881 

.000  926  7-11 

1080 

1  166  400 

1  259  712  000 

32.863  : 

10.259  8557 

.000  925  9-259 

1081 

1  168  561 

1  263  214  441 

323785644 

10.263  0213 

.000  925  0694 

1082 

117    724 

6  723  368 

32.893  7684 

10.266  1850 

.000  924  2144 

1083 

1  172  889 

1  270  238  787 

32.908  9653 

10.269  3467 

.000  9233610 

1084 

1  17" 

1  273  760  704 

32.924  1553 

10.272  5065 

.000  922  5092 

1085 

1  177  22S 

1  277  289  125 

32.939  3382 

10.2756644 

.000  921  6590 

1  179  396 

1  280824056 

32.9545141 

10.2788203 

.000  920  M<  "3 

1087 

1  181  569 

1284  365  503 

32.969  6830 

10.2S1  9743 

.000  919  9632 

1  183  744 

1  287  913472 

32.984  8450 

10.2851264 

.000  919  1176 

10S9 

1  185  921 

1  291  467  969 

33.000  0000 

10.288  2765 

.000  9ls  27  6 

1090 

118>  1"" 

1  295  029  000 

33.015  1480 

10.2V1  4247 

.000  917  4312 

1091 

1  190  281 

1  298  596  571 

0302891 

10.294  5709 

.000  916  5903 

1092 

1  192 

1302  17 

;',  . 

10.297  71 

.000  915  7 -.OQ 

542 


Towers  and  Roots. 


Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

1093 

1 194  649 

1  305  751  357 

33.060  5505 

10.300  8577 

.000  914  9131 

1094 

1  196  836 

1  309  338  584 

33.075  67i  is 

10.303  9982 

.000  914  0768 

1095 

1  199  025 

1  312  932  375 

33.090  78 12 

10.307  1368 

.000  913  2420 

1096 

1  201  216 

1  316  532  736 

33.105  8907 

10.310  2735 

.000  912  4008 

1097 

1  203  409 

1  320  139  673 

33.120  9903 

10.313  4083 

.000  911  5770 

1098 

1  205  604 

1  323  753  192 

33.136  0830 

10.316  5411 

.000  910  7468 

1099 

1  207  801 

1  327  373  299 

33.151 16S9 

10.319  6721 

.000  909  9181 

1100 

1  210  000 

1  331  000  000 

33.166  2479 

10.322  8012 

.000  909  0909 

1101 

1  212  201 

1  334  633  301 

33.181  3200 

10.325  9284 

.000  908  2652 

1102 

1  214  404 

1  338  273  208 

33.196  3853 

10.329  0537 

.000  907  4410 

1103 

1  216  609 

1  341  919  727 

33.211  4438 

10.332  1770 

.000  906  6183 

1104 

1  218  816 

1  345  572  864 

33.226  6955 

10.335  2985 

.000  905  7971 

1105 

1  221  025 

1  349  232  625 

33.241  5403 

10.338  4181 

.000  904  9774 

1106 

1  223  236 

1  352  899  016 

33.256  5783 

10.341  5358 

.000  904  1591 

1107 

1  225  449 

1  356  572  043 

33.271  6095 

10.344  6517 

.000  903  3424 

1108 

1  227  664 

1  360  251  712 

33.286  6339 

10.347  7657 

.000  902  5271 

1109 

1  229  881 

1  363  938  029 

33.301  6516 

10.350  8778 

.000  901  7133 

1110 

1  232  100 

1  367  631  000 

33.316  6625 

10.353  9880 

.000  900  9009 

1111 

1  234  321 

1  371  330  631 

33.331  6666 

10.357  0964 

.000  900  0900 

1112 

1  236  544 

1  375  036  928 

33.346  6640 

10.360  2029 

.000  899  2806 

1113 

1  238  769 

1  378  749  897 

33.361  6546 

10.363  3076 

.000  898  4726 

1114 

1  240  996 

1  382  469  544 

33.376  6385 

10.366  4103 

.000  897  6661 

1115 

1  243  225 

1  386  195  875 

33.391  6157 

10.369  5113 

.000  896  8610 

1116 

1  245  456 

1  389  928  896 

33.406  5862 

10.372  6103 

.000  896  0753 

1117 

1  247  689 

1  393  668  613 

33.421  5499 

10.375  7076 

.000  895  2551 

1118 

1  249  924 

1  397  415  032 

33.436  5070 

10.378  8030 

.000  894  4544 

1119 

1  252  161 

1  401  168  159 

33.451  4573 

10.381  8965 

.000  893  6550 

1120 

1  254  400 

1  404  928  000 

33.466  4011 

10.384  9882 

.000  892  8571 

1121 

1  256  641 

1  408  694  561 

33.481  3381 

10.388  0781 

.000  896  0607 

1122 

1  258  884 

1  412  467  848 

33.496  2684 

10.391  1661 

.000  892  2656 

1123 

1  261 129 

1  416  247  867 

33.511  1921 

10.394  2527 

.000  890  4720 

1124 

1  263  376 

1  420  034  624 

33.526  1092 

10.397  3366 

.000  889  6797 

1125 

1  265  625 

1  423  828  125 

33.541  0196 

10.400  4192 

.000  888  8889 

1126 

1  267  876 

1  427  628  376 

33.555  9234 

10.403  4999 

.000  888  0995 

1127 

1  270  129 

1  431  435  383 

33.570  8206 

10.406  5787 

.000  887  3114 

1128 

1  272  384 

1  435  249  152 

33.585  7112 

10.409  6557 

.000  886  5248 

1129 

1  274  641 

1  439  069  689 

33.600  5952 

10.412  7310 

.000  885  7396 

1130 

1  276  900 

1  442  897  000 

33.615  4726 

10.415  8044 

.000  884  9558 

1131 

1  279  161 

1  446  731  091 

33.630  3434 

10.418  8760 

.000  884  1733 

1132 

1  281  424 

1  450  571  968 

33.645  2077 

10.421  9458 

.000  883  3922 

1133 

1  283  689 

1  454  419  637 

33.660  0653 

10.425  0138 

.000  882  6125 

1134 

1  285  956 

1  458  274  104 

33.674  9165 

10.428  0800 

.000  881  8342 

1135 

1  288  225 

1  462  135  375 

33.689  7610 

10.431  1443 

.000  881  0573 

1136 

1  290  496 

1  466  003  456 

33.704  5991 

10.434  2069 

.000  880  2817 

1137 

1  292  769 

1  469  878  353 

33.717  4306 

10.437  2677 

.000  879  5075 

1138 

1  295  044 

1  473  760  072 

33.734  0556 

10.440  3677 

.000  878  7346 

1139 

1  297  321 

1  477  648  619 

33.749  0741 

10.443  3839 

.000  877  9631 

1140 

1  299  600 

1  4S1  544  000 

33.763  8860 

10.446  4393 

.000  877  1930 

1141 

1  301  881 

1  485  446  221 

33.778  6915 

10.449  4929 

.000  876  4242 

1142 

1  304  164 

1  489  355  288 

33.793  4905 

10.452  5448 

.000  875  6567 

1143 

1  306  449 

1  493  271  207 

33.808  2830 

10.455  5948 

.000  874  8906 

1144 

1  308  736 

1  497  193  984 

33.823  0691 

10.458  6431 

.000  874  1259 

Powers  and  Roots. 


54:1 


Number. 

Squares. 

Cu'< 

I  l: 

r  Boote. 

Reciprocals. 

11-15 

1  311  025 

1  501  123  625 

33.837  8486 

10.461  1 

.0008733624 

1 1 16 

1  813  816 

1505080  1  6 

33.8526218 

10.464  7343 

.000  872  6003 

HIT 

1  315 

1  509  003  523 

33.867  3884 

10.467  777.: 

.000  871 

1148 

1  317 

1  512  953  792 

33.882  H-7 

10.4708158 

.000871     - 

1119 

1  32 

1  516  910949 

-'."•.9025 

10.17:;  - 

.000  870  8220 

1150 

1  322  .500 

1  520  875000 

33.911  6499 

10.4768955 

.000  569  :.<::-l 

1151 

1  324  -   1 

1  524  845  951 

33.926  3909 

10.479  931 4 

.000  K68  8097 

1152 

1  327  104 

1  528  823  808 

33.941  1255 

10.4829 

.000  868  0556 

1153 

1  329  409 

1  532808577 

33.955  8537 

10.485  9980 

.000.-6,7  3027 

1154 

1     ;l  716 

1536800  264 

33.970  5755 

10.4890286 

.000  8665511 

1155 

1  334  025 

1  540  798  57 

33.985  2910 

10.492  0575 

.000  865  8009 

1156 

1  336  336 

1544  804  416 

31. 000  0000 

10.4950847 

.000  865  0519 

1157 

1  338  649 

1  548816893 

34.014  7027 

10.4981101 

.000864  3042 

1158 

1  MO  964 

1  552  836  312 

34.0293990 

10.501  1337 

.000  863  5579 

1159 

1  343  281 

1  556  862  679 

34.044  0890 

10.504  1556 

.000  862  8128 

1160 

1  345600 

1  560  896  000 

34.058  7727 

10.507  1757 

.000  862  0690 

1161 

1  347  921 

1  564  936  281 

34.073  4501 

10.5101942 

.000  861  3264 

1162 

1350244 

1  56.X  <>*3  5> 

34.0.^1211 

10.513  2109 

.000  860 

116S 

1  :  .52  569 

1  573  037747 

34.012  7858 

10.516  2259 

.000  859  M 52 

1164- 

1  354  896 

1  577  098  944 

34.117  4442 

10.519  2391 

.000  859  1065 

1165 

1357  225 

1  581 167  125 

31.132  0963 

10.522  2506 

.000  8-58  3691 

1166 

1  359  556 

1585  242296 

34.146  7122 

10.525  2604 

.000  857  6329 

1167 

1  361  B89 

1  589  324  463 

34.161  3817 

10.528  2685 

.000  856  8980 

1168 

1  364  224 

1  593  413632 

34.1760150 

10.5312749 

.000  856  16.11 

1169 

1  366  561 

1  597  509  809 

34.190  6120 

10.534  2795 

.000  855  4320 

1170 

1  368900 

1  601  613  000 

34.205  2627 

10.537  2825 

.000  854  7009 

1171 

1  371  241 

1  605  723  211 

34.219  8773 

10.540  2837 

.000  853  9710 

1172 

1  373  584 

1609  840  4!- 

34.234  4855 

10.543  2832 

.000  853  2423 

1173 

1  375  929 

1  613  964  717 

34.249  087 

10.546  2810 

.000  852  51 49 

1174 

1  378  276 

1618  096C2I 

34.263  6834 

10..549  2771 

.000*5]  7888 

1175 

1  380  62-5 

1  622  234  375 

34.278  2730 

10.552  2715 

.000  851  0638 

1176 

1  182976 

1  626  379  776 

34.2928564 

10.555  2642 

.000  850  3401 

1177 

1  385329 

1  630  532  2:;:: 

34.307  4336 

10.558  2552 

.000  849  6177 

1178 

1387  684 

1  634  691  752 

34.3220046 

10.5612445 

.000  848  8964 

1179 

1390  041 

1  638858  339 

34.336  5694 

10.564  2322 

.000  848  1764 

1180 

1  392  400 

1  643  032  000 

34.351  1281 

10.5r,7  2181 

.000  847  1576 

11-1 

1  394  761 

1  647212741 

34.3656805 

10.570  2024 

.000  846  7401 

1182 

1  397  124 

1  651  400  568 

34.380  - 

10.573  1849 

.000  846  0237 

1183 

1  399  489 

1  655  595487 

34.394  7670 

10.576,  1658 

.000  845  3085 

1184 

1401856 

1  659797  504 

34.409  3011 

10.5791449 

.000  844  5946 

1185 

1  mi  225 

1  664  006 

34.423  8289 

10.582  1225 

.000  843  8819 

1186 

1  406  596 

1  668  222  856 

34.4383507 

10.5-5(1'..-:; 

.000  843  1703 

11-7 

1  10S969 

1  672  446  203 

34.4528663 

10.588  0725 

.000  S42  4600 

1188 

1  111344 

.  676  672 

S4.4673759 

10.591  0450 

.000-11 

1189 

1  113  721 

1  91 1  629 

34.481  8793 

10.594  0158 

.000  Ml  0429 

1190 

I  416  100 

5  159  000 

34.496  3766 

10.596  9850 

.000  8403361 

1191 

1  11-  181 

•  110871 

S  1.510  8678 

10.599  9525 

.0008391 

U92 

1  12 



34.525  3530 

10.602  91-1 

.000  838  924  2 

1193 

1  123  249 

l  <:•.<:  9  60  <: 

34.5398321 

10.605  8826 

.000  838  - 

1194 

1  125 

1  702209  384 

J543051 

10.6088451 

.000  837 

1195 

-  025 

1  706  489  875 

• 

10.611  B 

.000  836  - 

11% 

:  ;    I  116 

1  710  777  536 

34.583  2329 

10.614  : 

.000  836  1204 

544 


Powers  and  Roots. 


Number. 


1197 
1198 
1199 
1200 
1201 
1202 
1203 
1204 
1205 
1206 
1207 
1208 
1209 
1210 
1211 
1212 
1213 
1214 
1215 
1216 
1217 
1218 
1219 
1220 
1221 
1222 
1223 
1224 
1225 
1226 
1227 
1228 
1229 
1230 
1231 
1232 
1233 
1234 
1235 
1236 
1237 
1238 
1239 
1240 
1241 
1242 
1243 
1244 
1245 
1246 
1247 
1248 


Squares. 


1  432  809 
1  435  204 
1  437  601 
1  440  000 
1  442  401 
1  444  804 
1  447  209 
1  449  616 
1  452  025 
1  454  436 
1  456  849 
1  459  264 
1  461  681 
1  464  100 
1  466  521 
1  468  944 
1  471  369 
1  473  796 
1  476  225 
1  478  656 
1  481  089 
1  483  524 
1  485  961 
1  488  400 
1  490  841 
1  493  284 
1  495  729 
1  498  176 
1  500  625 
1  503  276 
1  505  529 
1  507  984 
1  510  441 
1  512  900 
1  515  361 
1  517  824 
1  520  289 
1  522  756 
1  525  225 
1  527  696 
1  530  169 
1  532  644 
1  535  121 
1  537  600 
1  540  081 
1  542  564 
1  545  049 
1  547  536 
1  550  025 
1  552  516 
1  555  009 
1  557  504 


Cubes. 


1  715  072  373 
1  719  374  392 
1  723  683  599 


728  000  000 
732  323  601 
736  654  408 
740  992  427 
745  337  664 
749  690  125 
754  049  816 
1  758  416  743 
1  762  790  912 
1  767  172  329 
1  771  561  000 
1  775  956  931 
1  780  360  128 
1  784  770  597 
1  789  188  344 
1  793  613  375 
1  798  045  696 
1  802  485  313 
1  806  932  232 
1  811  386  459 
1  815  848  000 
1  820  316  861 
1  824  793  048 
1  829  276  567 
1  833  764  247 
1  838  265  625 
1  842  771 176 
1  847  284  083 
1  851  804  352 
1  856  331  989 
1  860  867  000 
1  865  409  391 
1  869  959  168 
1  874  516  337 
1  879  080  904 
1  883  652  875 
1  888  232  256 
1  892  819  053 
1  897  413  272 
1  902  014  919 
1  906  624  000 
1  911  240  521 
1  915  864  488 
1  920  495  907 
1  925  134  784 
1  929  781  125 
1  934  434  936 
1  939  096  223 
1  943  764  992 


V  Roots. 


34.597  6879 
34.612  1366 
34.626  5794 
34.641  0162 
34.655  4469 
34.669  8716 
34.684  2904 
34.698  7031 
34.713  1099 
34.727  5107 
34.741  9055 
34.756  2944 
34.770  6773 
34.785  0543 
34.799  4253 
34.813  7904 
34.828  1495 
34.842  5028 
34.856  8501 
34.871  1915 
34.885  5271 
34.899  8567 
34.914  1805 
34.928  4984 
34.942  8104 
34.957  1166 
34.971  4169 
34.985  7114 
35.000  0000 
35.014  2828 
35.028  5598 
35.042  8309 
35.057  0963 
35.071  3558 
35.085  6096 
35.099  8575 
35.114  0997 
35.128  3361 
35.142  5668 
35.156  7917 
35.171  0108 
35.185  2242 
35.199  4318 
35.213  6337 
35.227  8299 
35.242  0204 
35.256  2051 
35.270  3842 
35.284  5575 
35.298  7252 
35.312  8872 
35.327  0435 


Roots. 


10.617  7228 
10.620  6788 
10.623  6331 
10.626  5857 
10.629  5367 
10.632  4860 
10.635  4338 
10.638  3799 
10.641  3244 
10.644  2672 
10.647  2085 
10.650  1480 
10.653  0860 
10.656  0223 
10.658  9570 
10.661  8902 
10.664  8217 
10.667  7516 
10.670  6799 
10.673  6066 
10.676  5317 
10.679  4552 
10.682  3771 
10.685  2973 
10.688  2160 
10.691 1331 
10.694  0486 
10.696  9625 
10.699  8748 
10.702  7855 
10.705  6947 
10.708  6023 
10.711  5083 
10.714  4127 
10.717  3155 
10.720  2168 
10.723  1165 
10.726  0146 
10.728  9112 
10.731  8062 
10.734  6997 
10.737  5916 
10.740  4819 
10.743  3707 
10.746  2579 
10.749  1436 
10.752  0277 
10.754  9103 
10.757  7913 
10.760  6708 
10.763  5488 
10.766  4252 


Reciprocals. 


.000  835  4219 
.000  834  7245 
.000  834  0284 
.000  833  3333 
.000  832  6395 
.000  831  9468 
.000  831  2552 
.000  830  5648 
.000  829  8755 
.000  829  1874 
.000  828  5004 
.000  827  8146 
.000  827  1299 
.000  826  4463 
.000  825  7638 
.000  825  0825 
.000  824  4023 
.000  823  7232 
.000  823  0453 
.000  822  3684 
.000  821  6927 
.000  821  0181 
.000  820  3445 
.000  819  6721 
.000  819  0008 
.000  818  3306 
.000  817  6615 
.000  816  9935 
.000  816  3265 
.000  815  6607 
000  814  9959 
.000  814  3322 
.000  813  6696 
.000  813  0081 
.000  812  3477 
.000  811  6883 
.000  811  0300 
.000  810  3728 
.000  809  7166 
.000  809  0615 
.000  808  4074 
.000  807  7544 
.000  807  1025 
.000  806  4516 
.000  805  8018 
.000  805  1530 
.000  804  5052 
.000  803  8585 
.000  803  2129 
.000  802  5682 
.000  801  9246 
.000  801  2821 


Powers 

and  Roots. 

54-'. 

Number. 

Squares. 

Cul 

i  l;    be 

t  K     • 

Reciprocals. 

1249 

1  560  001  ' 

1948  44121'.* 

35.341 1941 

10.769  3001 

.000  800  6405 

1250 

1562  500 

1  953  125  000 

.391 

10.772  1 

.000  800  0000 

1251 

1565  001 

1  957  816  251 

35.369  47- 1 

10.775  • 

.000  799  3605 

1252 

1567  504 

1  962  515  008 

35.3S3  6 120 

10.777  9156 

.000  798  7220 

1253 

1570  009 

1  967  221  277 

35.397  7400 

10.7S0  7-1:: 

.000  798  0846 

1254 

1  572  516 

1  971  9:55  064 

111  8624 

10.783  6516 

.000  797  1 182 

1255 

1  575  025 

1  976  656  375 

35.425  9; 

M.7K6  5173 

.000  796  8127 

1256 

1  577  536 

19S1  385  2  16 

1 10  0903 

10.789  3.-i:. 

.000  7961783 

1257 

1580  049 

1  986  121  593 

35. 1 "t  1958 

10.7922441 

.000  795  5449 

1258 

1  582 

1990S6.">:.1J 

35.468  2 

10.7'.'-.  1 

.000  794  9126 

1259 

15S5  081 

1  995  616  979 

;  32  3900 

10.797  9649 

.000  794  2-12 

1260 

1587  600 

2  000  376  000 

35.496  4787 

10.800-- 

.000  793  6-508 

1261 

1590  121 

2005142581 

35.5105618 

10.803  6797 

.000  793  0214 

1262 

1592644 

2  009  916  728 

35.524  6393 

10.806  5 

.000  792  3930 

1263 

1  595  10.9 

2  014  698  447 

35.538  7113 

10.809  3-- l 

.000  791  7656 

1264 

1  597  6% 

2  019  4-7  711 

35.552  7777 

10.8122404 

.000  791 1392 

1  600  225 

2  024  28 1  625 

35.566  8385 

10.815  0909 

.000  790  5138 

1266 

1602  756 

2  029  089  096 

35.580  8937 

10.817  9400 

.000  789  8894 

1267 

1605  289 

2  033  901  163 

35.594  9434 

10.820  7876 

.000  789  2660 

12  - 

1  607  824 

2  038  720  832 

35.608  9876 

10.823  f , 

.000  788  6435 

1269 

1  610  361 

2  043  548  109 

35.623  0262 

10.826  47-2 

.000  788  0221 

1270 

1  612  900 

2  048  383  000 

35.637  0593 

10.829  3213 

.000  787  4016 

1271 

1  615  441 

2  053  225  511 

35.651  0S69 

10.832  1629 

.000  7S6  7-21 

1272 

1  617  98  l 

2  058  075  648 

35.6651090 

10.835  0030 

.000  786  1635 

1273 

1  620  529 

2  062  933  417 

35.679  1255 

10.837  8416 

.000  785  5460 

1274 

1  623  076 

2067798824 

35.693  1366 

10.840  6788 

.000  784  9294 

1275 

1  625  625 

2  072  671  875 

35.707  1421 

10.843  5144 

.000  784  3137 

1276 

1  628  176 

2  077  552    J 

35.721  1422 

10.846  3485 

.000  783  6991 

1277 

1  630  729 

2  082  440  933 

35.735  1367 

10.849  1812 

.000  783  0854 

1278 

1633  284 

2  087  336  952 

35.749  1258 

10.852  0125 

.000  7S2  4726 

1279 

1635  841 

2  092  240  639 

35.763  1095 

10.854  8422 

.000  781  8608 

1280 

1638  400 

2  097  152  000 

35.777  0876 

10.857  6704 

.000  781  2500 

1281 

1  640  961 

2  102  071  Ml 

35.791  0603 

10.860  4972 

.000  780  6401 

1282 

1  643  524 

2  106  997  :■  - 

35.805  0276 

10.863  3225 

.000  780  0312 

1283 

1646  089 

2111932  1-7 

35.818  9894 

10.866  14-54 

.000  779  4232 

1284 

1648  656 

2116  874  304 

35.832  9457 

10.868  9687 

.000  778  8162 

1285 

1  651  225 

2  121  S24  125 

35.846  8966 

10.871  7897 

.000  778  2101 

1286 

1  653  7% 

2  126  781656 

35.860  8 121 

10.874  6091 

.000  777  6050 

1287 

1656  369 

2  131  746  903 

35.S74  7822 

10.S77  4271 

.000  777  0008 

1288 

1658  944 

2136719  872 

35.888  7169 

10.880  2436 

.000  776  3975 

1289 

1  661  521 

2  141  700  569 

35.902  6461 

10.883  0587 

.000  775  7952 

1290 

1  664  100 

2  1 16  689  000 

35.916  5699 

10.885- 

.000  775  1938 

1291 

1666  681 

2  151  &.*5  171 

35.930  4S84 

10.888  6845 

.000  774  5933 

1292 

1   669    -       : 

2  156  689  088 

35.944  4015 

10.891  4952 

.000  773  9938 

1293 

1  671  849 

2  lr.l  700  757 

35.958  3092 

10.894  3044 

.000  773  3952 

1294 

1  674  436 

2  166  720  184 

35.972  211'- 

10.*'.'7  1123 

.000  772  7975 

1296 

1  677 

2  171  747  375 

35.986H'-! 

10.899  9186 

.000  772  2008 

1296 

1  679  616 

2  176  7-2  336 

36.000  0000 

10.902  7. 

.000  771  6049 

1297 

1682  209 

■  073 

36.013  8862 

10.90-5  : 

.000  771  0100 

1296 

1684  804 

2  186  875  592 

36.027  7671 

10.908  3290 

.000  770  4160 

1299 

1  687  401 

2  191  933  899 

36.041  6426 

10.911  1296 

.000  769  • 

1300 

1690  000 

2  197  000  000 

36.055  5128 

10.913  9287 

.000  769  2308 

>46 


Powers  and  Roots. 


Number. 

Squares. 

Cubes. 

V  Roots. 

f  Koots. 

Reciprocals. 

1301 

1692  601 

2  202  073  901 

36.069  3776 

10.916  7265 

.000  768  6395 

1302 

1  695  204 

2  207  155  60S 

36.083  2371 

10.919  5228 

.000  768  0492 

1303 

1  697  809 

2  212  245  127 

36.097  0913 

10.922  3177 

.000  767  4579 

1301 

1700  416 

2  217  342  464 

36.110  9402 

10.925  1111 

.000  766  8712 

1305 

1  703  025 

2  222  447  625 

36.124  7837 

10.927  9031 

.000  766  2835 

1306 

1  705  636 

2  227  560  616 

36.138  6220 

10.930  6937 

.000  765  6968 

1307 

1  708  249 

2  232  681  443 

36.152  4550 

10.933  4829 

.000  765  1109 

1308 

1  710  864 

2  237  810  112 

36.166  2826 

10.936  2706 

.000  764  5260 

1309 

1  713  481 

2  242  946  629 

36.180  1050 

10.939  0569 

.000  763  9419 

1310 

1  716  100 

2  248  091  000 

36.193  9221 

10.941  8418 

.000  763  3588 

1311 

1  718  721 

2  253  243  231 

36.207  7340 

10.944  6253 

.000  762  7765 

1312 

1  721  344 

2  258  403  328 

36.221  5406 

10.947  5074 

.000  762  1951 

1313 

1  723  969 

2  263  571  297 

36.235  3419 

10.950  1880 

.000  761  6446 

1314 

1  726  596 

2  268  747  144 

36.249  1379 

10.952  9673 

.000  761  0350 

1315 

1  729  225 

2  273  930  875 

36.262  6287 

10.955  7451 

.000  760  4563 

1316 

1  731  856 

2  279  122  496 

36.276  7143 

10.958  5215 

.000  759  8784 

1317 

1  734  489 

2  284  322  013 

36.290  4246 

10.961  2965 

.000  759  3014 

1318 

1  737  124 

2  289  529  432 

36.304  2697 

10.964  0701 

.000  758  7253 

1319 

1  739  761 

2  294  744  759 

36.318  0396 

10.906  8423 

.000  758  1501 

1320 

1  742  400 

2  299  968  000 

36.331  8042 

10.969  6131 

.000  757  5758 

1321 

1  745  041 

2  305  199  161 

36.345  5637 

10.972  3825 

.000  757  0023 

1322 

1  747  684 

2  310  438  248 

36.359  3179 

10.975  1505 

.000  756  4297 

1323 

1  750  329 

2  315  685  267 

36.373  0670 

10.977  9171 

.000  755  8579 

1324 

1  752  976 

2  320  940  224 

36.386  8108 

10.980  6823 

.000  755  2870 

1325 

1  755  625 

2  326  203  125 

36.400  5494 

10.983  4462 

.000  754  7170 

1326 

1  758  276 

2  331  473  976 

36.414  2829 

10.986  2086 

.000  754  1478 

1327 

1  760  929 

2  336  752  783 

36.428  0112 

10.988  9696 

.000  753  5795 

1328 

1  763  584 

2  342  039  552 

36.441  7343 

10.991  7293 

.000  753  0120 

.  1329 

1  766  241 

2  347  334  289 

36.455  4523 

10.994  4876 

.000  752  4454 

1330 

•  1  768  900 

2  352  637  000 

36.469  1650 

10.997  2445 

.000  751  8797 

1331 

1  771  561 

2  357  947  691 

36.482  8727 

11.000  0000 

.000  751  3148 

1332 

1  774  224 

2  363  266  368 

36.496  5752 

11.002  7541 

.000  750  7508 

1333 

1  776  889 

2  368  593  037 

36.510  2725 

11.005  5069 

.000  750  1875 

1334 

1  779  556 

2  373  927  704 

36.523  9647 

11.008  2583 

.000  749  6252 

1335 

1  782  225 

2  379  270  375 

36.537  6518 

11.011  0082 

.000  749  0637 

1336 

1  784  896 

2  3S4  621  056 

36.551  3388 

11.013  7569 

.000  748  5030 

1337 

1  787  569 

2  389  979  753 

36.565  0106 

11.016  5041 

.000  747  9432 

1338 

1  790  244 

2  395  346  472 

36.578  6823 

11.019  2500 

.000  747  3842 

1339 

1  792  921 

2  400  721  219 

36.592  3489 

11.021  9945 

.000  746  8260 

1340 

1  795  600 

2  406  104  000 

36.606  0104 

11.024  7377 

.000  746  2687 

1341 

1  798  281 

2  411  494  821 

36.619  6668 

11.027  4795 

.000  745  7122 

1342 

1  800  964 

2  416  893  688 

36.633  3181 

11.030  2199 

.000  745  1565 

1343 

1  803  649 

2  422  300  607 

36.646  9141 

11.032  9590 

.000  744  6016 

1344 

1  806  336 

2  427  715  584 

.  36.660  6056 

11.035  6967 

.000  744  047G 

1345 

1  809  025 

2  433  138  625 

36.674  2416 

11.038  4330 

.000  743  4944 

1346 

1  811  716 

2  438  569  736 

36.687  8726 

11.041 1680 

.000  742  9421 

1347 

1  814  409 

2  444  008  923 

36.701  4986 

11.043  9017 

.000  742  3905 

1348 

1  817  104 

2  449  456  192 

36.715  1195 

11.046  6339 

.000  741  8398 

1349 

1  819  801 

2  454  911  549 

36.728  7353 

11.049  3649 

.000  741  2898 

1350 

1  822  500 

2  460  375  000 

36.742  3461 

11.052  0945 

.000  740  7407 

1351 

1  825  201 

2  465  846  551 

36.755  9519 

11.054  8227 

.000  740  1924 

1352 

1  827  904 

2  471  326  208 

36.769  5526 

11.057  5497 

.000  739  6450 

Powers 

and  Roots. 

547 

Number. 

Squares. 

Cui 

•Boots, 

f  RC 

Reciprocals. 

1353 

1  830  609 

2  476  813  977 

36.7831483 

11.0602752 

.000  739  0983 

L354 

1  833  316 

2  182  309  864 

36.796  7390 

11.0629994 

.000  788 

1355 

1  836  025 

2  187  813875 

36.810  3246 

11.065  7222 

.000  738  0074 

1366 

1  838 

2493  326016 

36.823  9053 

11.0684437 

.000  7: 17  1631 

L357 

1  Ml  419 

2  198846  293 

86.837  4809 

11.071  1639 

.000  736  91  '.'7 

1358 

1844  164 

2  504:171712 

36.851  0515 

11.0738828 

.000736  3770 

1359 

1846  881 

2  509  911  27'.) 

36.864  6172 

11.0766003 

.000  735 

1360 

1  - 19  600 

2515456000 

36.878  177s 

11.079  3165 

.000735  2941 

1361 

1852321 

2  .".21008  881 

36.8917:::". 

11.0820314 

.000  734  7.".:  (9 

1362 

1  355044 

2  526  569  928 

36.905  28 12 

11.084  7449 

.000734  2144 

1363 

1  -  57  769 

2  532139  117 

36.918  8299 

11.087  4571 

.000  733  6757 

1364 

1  860  196 

2537  716  544 

36.932  3706 

11.090  1679 

.000  7::::  L378 

1365 

1  363  225 

2  543  302125 

36.945  9064 

11.092  877:. 

.000  732  6007 

1366 

1  865  956 

2  548  895  896 

36.959  4372 

11.0955857 

.000  732  0644 

1367 

1  868  689 

2554  497  863 

36.972  9631 

11.098  2926 

.000  731  5289 

1  871  424 

2  560108032 

36.986  is  10 

11.100  9982 

.000  730  9942 

1369 

1  874  161 

2  565  720  409 

:  :7.ooo  oooo 

11.103  7025 

.000  730  4602 

1370 

1876  900 

2  571  353  000 

37.013  5110 

11.106  40.".  1 

.000  729  9270 

1371 

1  879  641 

2  576  987  81 1 

37.027  0172 

11.109  1070 

.000  729  3946 

1372 

1  882  3S4 

2  582  630  Ms 

37.040  5184 

11.1118073 

.000  728  8630 

1373 

1  885  129 

2  588  282 117 

37.054  01 16 

11.1115061 

.000  728  3321 

1374 

1  887  876 

2  593  941624 

37.067  5060 

11.117  2041 

.000  727  8020 

1375 

1  890  625 

2  599  609  375 

37.089  9924 

11.119  9004 

.000  727  2727 

1376 

1  893  376 

2605  285  376 

37.091  4740 

11.122  5955 

.000  726  7442 

1377 

1  S96  129 

2  610  969  633 

37.107  9506 

11.125  2893 

.000  726  2164 

1378 

1  898  8S4 

2616  662152 

37.121  4221 

11  127  9817 

.000  725  6894 

1379 

1  901  641 

2  622  362  939 

37.1348893 

11.130  6729 

.000  725  1632 

1380 

1904  400 

2  628072000 

37.1483512 

11.133  3628 

.000  724  6377 

1381 

1  907  161 

2  633  789341 

37.1618084 

11.136  051 1 

.000  724  1130 

1382 

1909  924 

2  639  514  968 

37.175  2606 

11.138  7386 

.000  723  5890 

1383 

1  912  689 

2  645  248887 

37.1S8  7079 

11.1414246 

.000  723  0658 

1384 

,  1  915  456 

2  650991104 

37.202  1505 

11.144  1093 

.000  722  5434 

1385 

1  91s  225 

2656741  625 

37.215  5881 

11.116  7926 

.000  722  0217 

1386 

1  920  996 

2  662  500  456 

37.229  0209 

11.1494717 

.000  721  5007 

1387 

1  923  769 

2  668  267  603 

37.242  4489 

11.152  1555 

.000  720  9805 

138s 

I  926  544 

2674  043072 

37.255  8720 

11.1548350 

.000  720  4611 

1389 

1  929  321 

2  G79  826  869 

37.269  2903 

11.157  5133 

.000  719  9124 

1390 

1  932100 

2  6S5  619  000 

37.282  7037 

11.160  1903 

.000  719  4215 

1391 

1931  B81 

2  691419  471 

37.296  1124 

11.1628659 

.000  718  9073 

1392 

l     [7  664 

2  697  228  288 

37.309  5162 

11.165  5403 

.000  718  3908 

1393 

1940  149 

2703  045457 

37.322  9152 

11.168  2134 

.000  717  8751 

1394 

1943  236 

2  71 «  870  984 

37.336  3094 

11.170  8852 

.000  717  3601 

1395 

1946025 

2  71 1  704  875 

37.3496988 

11.1735558 

.000  716  8459 

13% 

1  948  816 

2  720  M7  136 

37.363  0834 

11.176  2250 

.000  7163324 

1397 

1  951  609 

2  726  397  77:: 

::7.::7i'i  1632 

11.178  8930 

.000  715  8196 

1398 

1954  4<»1 

2  7::2  256  792 

37.389  8382 

11.1815598 

.000  715  3076 

1399 

1  '.'.-.7  2iil 

2738  124  199 

37.403  2084 

11.1842252 

.000  71 1  7963 

1400 

1  960  000 

2  7  1 1  000  000 

37.416  ( 

11.186  8894 

.000  71 1  2857 

1401 

1  '.".2  801 

2  7  19  884  201 

37.429  9345 

11.1895523 

.0007137759 

1 102 

1  965  604 

2  755  77l 

37.443  2904 

11.1922139 

.000  713  2668 

1403 

1  968  409 

2  761  677 

37.4566416 

11.194  8748 

.0007127584 

1404 

1  971  216 

2  767  587  264 

37.4699880 

11.197. 

.0007122507 

548 

Powers 

and  Roots 

• 

Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

1405 

1  974  025 

2  773  505  123 

37.483  3296 

11.200  1913 

.000  711  7438 

1406 

1  976  836 

2  779  431  416 

37.496  6665 

11.202  8479 

.000  711  2376 

1407 

1  979  649 

2  785  366  143 

37.509  9987 

11.205  5032 

.000  710  7321 

1408 

1  982  464 

2  791  309  312 

37.523  3261 

11.208  1573 

.000  710  2273 

1409 

1  985  281 

2  797  260  929 

37.536  6487 

11.210  8101 

.000  709  7232 

1410 

1  988  100 

2  803  221  000 

37.549  9667 

11.213  4617 

.000  709  2199 

1411 

1  990  921 

2  809  1S9  531 

37.563  2799 

11.216  1120 

.000  708  7172 

1412 

1  993  744 

2  815  166  528 

37.576  5885 

11.218  7611 

.000  708  2153 

1413 

1  996  569 

2  821 151  997 

37.589  8922 

11.221  4089 

.000  707  7141 

1414 

1  999  396 

2  827  145  944 

37.603  1913 

11.224  0054 

.000  707  2136 

1415 

2  002  225 

2  833  148  375 

37.616  4857 

11.226  7007 

.000  706  7138 

1416 

2  005  056 

2  839  159  296 

37.629  7754 

11.229  3448 

.000  706  2147 

1417 

2  007  889 

2  845  178  713 

37.643  0604 

11.231  9876 

.000  705  7163 

1418 

2  010  724 

2  851  206  632 

37.656  3407 

11.234  6292 

.000  705  2186 

1419 

2  013  561 

2  857  243  059 

37.669  6164 

11.237  2696 

.000  704  7216 

1420 

2  016  400 

2  863  288  000 

37.682  8874 

11.239  9087 

.000  704  2254 

1421 

2  019  241 

2  869  341  461 

37.696  1536 

11.242  5465 

.000  703  7298 

1422 

2  022  084 

2  875  403  448 

37.709  4153 

11.245  1831 

.000  703  2349 

1423 

2  024  929 

2  881  473  967 

37.722  6722 

11.247  8185 

.000  702  7407 

1424 

2  027  776 

2  887  553  024 

37.735  9245 

11.250  4527 

.000  702  2472 

1425 

2  030  625 

2  893  640  625 

37.749  1722 

11.253  0856 

.000  701  7544 

1426 

2  033  476 

2  899  736  776 

37.762  4152 

11.255  7173 

.000  701  2623 

1427 

2  036  329 

2  905  841  483 

37.775  6535 

11.258  3478 

.000  700  7708 

1428 

2  039  184 

2  911  954  752 

37.788  8873 

11.260  9770 

.000  700  2801 

1429 

2  042  041 

2  918  076  589 

37.802  1163 

11.263  6050 

.000  699  7901 

1430 

2  044  900 

2  924  207  000 

37.815  3408 

11.266  2318 

.000  699  3007 

1431 

2  047  761 

2  930  345  991 

37.828  5606 

11.268  8573 

.000  698  8120 

1432 

2  050  624 

2  936  493  568 

37.841  7759 

11.271  4816 

.000  698  3240 

1433 

2  053  489 

2  942  649  737 

37.854  9864 

11.274  1047 

.000  697  8367 

1434 

2  056  356 

2  948  814  504 

37.868  1924 

11.276  7266 

.000  697  3501 

1435 

2  059  225 

2  954  987  875 

37.881  3938 

11.279  3472 

.000  696  8641 

1436 

2  062  096 

2  961  169  856 

37.894  5906 

11.281  9666 

.000  696  3788 

1437 

2  064  969 

2  967  360  453 

37.907  7828 

11.2S4  5849 

.000  695  8942 

1438 

2  067  844 

2  973  559  672 

37.920  9704 

11.287  2019 

.000  695  4103 

1439 

2  070  721 

2  979  767  519 

37.934  1535 

11.289  8177 

.000  694  9270 

1440 

2  073  600 

2  985  984  000 

37.947  3319 

11.292  4323 

.000  694  4444 

1441 

2  076  481 

2  992  209  121 

37.960  5058 

11.295  0457 

.000  693  9625 

1442 

2  079  364 

2  998  442  888 

37.973  6751 

11.297  6579 

.000  693  4813 

1443 

2  082  249 

3  004  685  307 

37.986  8398 

11.300  2688 

.000  693  0007 

1444 

2  085  136 

3  010  936  384 

38.000  0000 

11.302  8786 

.000  692  5208 

1445 

2  088  025 

3  017  196  125 

38.013  1556 

11.305  4871 

.000  692  0415 

1446 

2  090  916 

3  023  464  536 

38.026  3067 

11.308  0945 

.000  691  5629 

1447 

2  093  809 

3  029  741  623 

38.039  4532 

11.310  7006 

.000  691  0850 

1448 

2  096  704 

3  036  027  392 

38.052  5952 

11.313  3056 

.000  690  6078 

1449 

2  099  601 

3  042  321  849 

38.065  7326 

11.315  9094 

.000  690  1312 

1450 

2  102  500 

3  048  625  000 

38.078  8655 

11.318  5119 

.000  689  6552 

1451 

2  105  401 

3  054  936  851 

38.091  9939 

11.321 1132 

.000  689  1799 

1452 

2  108  304 

3  061  257  408 

38.105  1178 

11.323  7134 

.000  688  7052 

1453 

2  111  209 

3  067  586  777 

38.118  2371 

11.326  3124 

.000  688  2312 

1454 

2  114  116 

3  073  924  664 

38.131  3519 

11.328  9102 

.000  687  7579 

1455 

2  117  025 

3  080  271  375 

38.144  4622 

11.331  5067 

.000  687  2852 

1456 

2  119  936 

3  086  626  816 

38.157  5681 

11.334  1022 

.000  686  8132 

Powers 

and  Roots 

540 

Number. 

Squares. 

Cubes. 

^Roots. 

f  Boots. 

Reciprocals. 

1457 

2  122  849 

3  092  990  993 

38.170  6693 

11.336  6964 

.000  686  3412 

1458 

2  125  764 

3  099  363  912 

38.183  7 

11.339  2894 

.000  685  8711 

1459 

2  128  681 

3  105  745  579 

38.196  8585 

11.341  8813 

.000  685  4010 

1460 

2131600 

3  112  136  000 

38.209  9463 

11.344  4719 

.000  6S4  9315 

1461 

2  134  521 

3  118  535  181 

38.223  0297 

11.347  061 1 

.000  684  4627 

1462 

2  l',7  444 

3  124  943  128 

38.236  1085 

11.349  6497 

.000  683  9945 

1463 

2  140  369 

3  131  359  847 

38.24'J  1829 

11.3522368 

.000  6S3  5270 

1464 

2  143  296 

8137  7-">344 

38.262  2529 

11.3548227 

.000  683  0601 

140". 

2  146  225 

3  144  219  625 

38.275  3184 

11.357  4075 

.000  682  5939 

1466 

2  149  156 

3  150  662  696 

38.288  3794 

11.359  9911 

.000  6821282 

1467 

2152089 

3  157  114  563 

38.301  4360 

11.362  5735 

.000  681  6633 

146S 

2  155  024 

3163  575  232 

38.314  4881 

11.3651547 

.000  681  1989 

1469 

2  157  961 

3  170  044  709 

38.327  5358 

11.367  7347 

.000  680  7352 

1470 

2  160  900 

3  176  523  000 

38.340  5790 

11.370  3136 

.000  680  2721 

1471 

2  163  841 

3  183  010  111 

38.353  6178 

11.372  8914 

.000  679  8097 

1472 

2  166  784 

3  1S9  506  048 

38.366  6522 

11.375  4679 

.000  679  3478 

1473 

2  169  729 

3196010817 

38.379  6821 

11.378  0433 

.000  678  8866 

1474 

2  172  676 

3  202  524  421 

38.392  7076 

11.3806175 

.000  678  4261 

1475 

2  175  625 

3  209  046  875 

38.405  7287 

11.383  1906 

.000  677  9661 

1476 

2  178  576 

3  215  578  176 

38.418  71.".  1 

11.3857625 

.000  677  5068 

■  1477 

2  1S1  529 

3  222  118  333 

38.431  7">77 

11.388  3332 

.000  677  0481 

1478 

2184  484 

3  228  667  352 

38.444  7656 

11.390  90-28 

.000  676  5900 

1479 

2  187  441 

3  235  225  239 

38.457  7691 

11.393  4712 

.000  676  1325 

1480 

2  190  400 

3  241  792  000 

38.470  7681 

11.396  0384 

.000  675  6757 

1481 

2  193  361 

3  248  367  641 

38.483  7627 

11.398  6045 

.000  675  2194 

1482 

2  196  324 

3  254  952  168 

38.496  7530 

11.4011695 

.000  674  7638 

1483 

2  199  289 

3  261  545  5S7 

38.509  7390 

11.403  7332 

.000  674  3088 

1484 

2  202  256 

3  268  147  904 

38.522  7206 

11.406  2959 

.000  673  8544 

1485 

2  205  225 

3  274  759  125 

38.535  6977 

11.4088574 

.000  673  4007 

1486 

2  208  196 

3  281  379  256 

38.548  6705 

11.4114177 

.000  672  9474 

1487 

2  211  169 

3  288  008  303 

38.561  6389 

11.413  9769 

.000  672  4950 

u- 

2  214  144 

3  294  646  272 

38.574  6030 

11.416  5349 

.000  672  0430 

1489 

2  217  121 

3  301  293  169 

38.587  5627 

11.419  0918 

.000  671  5917 

1490 

2  220100 

3  307  949  000 

38.600  5181 

11.420  6476 

.000  671 1409 

1491 

2  223  081 

3  314  613  771 

38.613  4691 

11.424  2022 

.000  670  6908 

1492 

2  226  064 

3  321  287  488 

38.626  4158 

11.426  7556 

.000  670  2413 

1493 

2  229  049 

3  327  970  157 

38.639  3582 

11.429  3079 

.000  669  7924 

1494 

2  232  036 

3  334  661  784 

38.652  2962 

11.4318591 

.000  669  3440 

1495 

2  235  025 

3  341  362  375 

38.665  2299 

11.434  4092 

.000  668  8963 

14% 

2  238  016 

3  348  071  936 

38.678  1593 

11.436  95S1 

.000  668  4492 

1497 

2  241009 

3  354  790  47:; 

38.691  0S43 

11.439  5059 

.000  668  0027 

1498 

2  244  004 

3  361  517  992 

38.704  0050 

11.442  0525 

.000  667  5567 

1499 

2  2 17  001 

3  368  254  499 

38.716  921 1 

11.444  5980 

.000  667  1114 

1500 

2250  000 

3  375  000  000 

38.729  8335 

11.447  1121 

.000  666  6667 

1501 

2  258  001 

3  381  754  .501 

38.742  7412 

11.449  6857 

.000  666  2225 

1502 

2  256  004 

3  388  518  008 

38.7556447 

11.452  2278 

.000  665  7790 

1503 

2  259  009 

3  395  290  527 

-  -  -  .  ■ 

11.15-17688 

.000  655  3360 

1504 

2  262  016 

3402072064 

38.781  4389 

11.157  3087 

.000  664  8936 

150.') 

2  265  025 

3  408  862 

38.794  3294 

11.459  8476 

.000  6644518 

1506 

2  268  036 

3  415  662  216 

38.807  2158 

11.462  3850 

.000  664  0106 

1507 

2  271  049 

3422470  843 

38.820  0978 

11.464  921") 

.000  663  5700 

1508 

2  274  064 

3  429  288  512 

38.832  9757 

11.467  4568 

.000  663  1300 

550 

Powers 

and  Roots 

Squares. 

Cubes. 

I7  Roots. 

Number. 

f  Roots. 

Reciprocals. 

1509 

2  277  081 

3  436  115  229 

38.845  8491 

11.469  9911 

.000  662  6905 

1510 

2  280  100 

3  442  951  000 

38.858  7184 

11.472  5242 

.000  662  2517 

1511 

2  283  121 

3  449  795  831 

38.871  5834 

11.475  0562 

.000  661  8134 

1512 

2  286  144 

3  456  649  728 

38.884  4442 

11.477  5871 

.000  661  3757 

1513 

2  289  169 

3  463  512  697 

38.897  3006 

11.480  1169 

.000  660  9385 

1514 

2  292  196 

3  470  384  744 

38.910  1529 

11.482  6455 

.000  660  5020 

1515 

2  295  225 

3  477  265  875 

38.923  0009 

11.485  1731 

.000  660  0660 

1516 

2  298  256 

3  484  156  096 

38.935  8447 

11.487  6995 

.000  659  6306 

1517 

2  301  289 

3  491  055  413 

38.948  6841 

11.490  2249 

.000  659  1958 

1518 

2  304  324 

3  597  963  832 

38.961  5194 

11.492  7491 

.000  658  7615 

1519 

2  307  361 

3  504  881  359 

38.974  3505 

11.495  2722 

.000  658  3278 

1520 

2  310  400 

3  511  808  000 

38.987  1774 

11.497  7942 

.000  657  8947 

1521 

2  313  441 

3  518  743  761 

39.000  0000 

11.500  3151 

.000  657  4622 

1522 

2  316  484 

3  525  688  648 

39.012  8184 

11.502  8348 

.000  657  0302 

1523 

2  319  529 

3  532  642  667 

39.025  6326 

11.505  3535 

.000  656  5988 

1524 

2  322  576 

3  539  605  824 

39.038  4426 

11.507  8711 

.000  656  1680 

1525 

2  325  625 

3  546  578  125 

39.051  2483 

11.510  3876 

.000  655  7377 

1526 

2  328  676 

3  553  559  576 

39.064  0499 

11.512  9030 

.000  655  3080 

1527 

2  331  729 

3  560  558  183 

39.076  8473 

11.515  4173 

.000  654  8788 

1528 

2  334  784 

3  567  549  552 

39.089  6406 

11.517  9305 

.000  654  4503 

1529 

2  337  841 

3  574  558  889 

39.102  4296 

11.520  4425 

.000  654  0222 

1530 

2  340  900 

3  581  577  000 

39.115  2144 

11.522  9535 

.000  653  5948 

1531 

2  343  961 

3  588  604  291 

39.127  9951 

11.525  4634 

.000  653  1679 

1532 

2  347  024 

3  595  640  768 

39.140  7716 

11.527  9722 

.000  652  7415 

1533 

2  350  089 

3  602  686  437 

39.153  5439 

11.530  4799 

.000  652  3157 

1534 

2  353  156 

3  609  741  304 

39.166  3120 

11.532  9865 

.000  651  8905 

1535 

2  356  225 

3  616  805  375 

39.179  0760 

11.535  4920 

.000  651  4658 

1536 

2  359  296 

3  623  878  656 

39.191  8359 

11.537  9965 

.000  651  0417 

1537 

2  362  369 

3  630  961 153 

39.204  5915 

11.540  4998 

.000  650  6181 

1538 

2  365  444 

3  638  052  872 

39.217  3431 

11.543  0021 

.000  650  1951 

1539 

2  368  521 

3  645  153  819 

39.230  0905 

11.545  5033 

.000  649  7726 

1540 

2  371  600 

3  652  264  000 

39.242  8337 

11.548  0034 

.000  649  3506 

1541 

2  374  681 

3  657  983  421 

39.255  5728 

11.550  5025 

.000  648  9293 

1542 

2  377  7G4 

3  666  512  088 

39.268  3078 

11.553  0004 

.000  648  5084 

1543 

2  380  849 

3  673  650  007 

39.281  0387 

11.555  4972 

.000  648  0881 

1544 

2  383  936 

3  6S0  797  184 

39.293  7654 

11.557  9931 

.000  647  6684 

1545 

2  387  025 

3  687  953  625 

39.306  4880 

11.560  4878 

.000  647  2492 

1546 

2  390  116 

3  695  119  336 

39.319  2065 

11.562  9815 

.000  646  8305 

1547 

2  393  209 

3  702  294  323 

39.331  9208 

11.565  4740 

.000  646  4124 

1548 

2  398  304 

3  709  478  592 

39.344  6311 

11.567  9655 

.000  645  9948 

1549 

2  399  401 

3  716  672  149 

39.357  3373 

11.570  4559 

.000  645  5778 

1550 

2  402  500 

3  723  875  000 

39.370  0394 

11.572  9453 

.000  645  1613 

1551 

2  405  601 

3  731  087  151 

39.382  7373 

11.575  4336 

.000  644  7453 

1552 

2  408  704 

3  738  308  608 

39.395  4312 

11.577  9208 

.000  644  3299 

1553 

2  411  809 

3  745  539  377 

39.408  1210 

11.5S0  4069 

.000  643  9150 

1554 

2  414  916 

3  752  779  464 

39.420  8067 

11.582  8919 

.000  643  5006 

1555 

2  418  025 

3  760  028  875 

39.433  4883 

11.585  3759 

.000  643  0868 

1556 

2  421  136 

3  767  287  616 

39.446  1658 

11.587  8588 

.000  642  6735 

1557 

2  424  249 

3  774  555  693 

39.458  8393 

11.590  3407 

.000  642  2608 

1558 

2  427  364 

3  781  833  112 

39.471  5087 

11.592  8215 

.000  641  8485 

1559 

2  430  481 

3  789  119  879 

39.484  1740 

11.595  3013 

.000  641  4368 

1560 

2  433  600 

3  796  416  000 

39.496  8353 

11.597  7799 

.000  641  0256 

Powers 

and  Roots 

551 

- 

Squares. 

Cul    - 

l  Boots. 

Number. 

t  Boots. 

Reciprocals. 

1561 

6  721 

3  803  721  1M 

39.509  4925 

11.6002576 

.000  640  01 50 

1562 

2439 

:;  Ml  036  328 

39.5221457 

11.6027342 

.000  010  2n  1'J 

1563 

2442969 

3818360547 

39..".: I  7948 

11.605  2097 

.000  639  7953 

1564 

2  446  096 

3825641  ill 

39.517  4399 

11.607  6841 

.000  639  3S62 

1565 

2  449  225 

-    1037125 

39.5600809 

11.610  157.". 

.000  638  9770 

1566 

2  152  356 

3  840  389  496 

39.572  717'.* 

11.612  6299 

.000  638  5696 

2  455  489 

3  847  751  263 

39.585: 

11.6151012 

.000  638  1021 

1568 

2  158  624 

3855123432 

39.597  97'.<7 

11.617  571". 

.000  637  7551 

1569 

2  461  761 

3  862  503  009 

39.610  6046 

11.620  0407 

.000  037 

1570 

2  461900 

3  869  883  000 

39.6232255 

11.622  5088 

.000  636  9427 

1571 

2  468  041 

3  877  2'.ij.lll 

39.6358424 

11.624  9759 

.000  636  5372 

1572 

2  471  184 

1  701  248 

39.648  4552 

11.6274420 

.000  636  1323 

1573 

2  174829 

3  892  119  1- ">7 

39.661  0640 

11.029  9070 

.000  635  7279 

1574 

2  477  476 

3  899  "17  224 

39.673  6688 

11.6323710 

.000  635  3240 

1575 

2  180625 

3  906  984  375 

39.6S6  2696 

11.634  8339 

.000  634  9206 

1576 

2  483  776 

3  914  430  976 

39.698  81  65 

11.637  2957 

.000  031517S 

1577 

2  486  929 

3  921  887  033 

39.711  4593 

11.639  7566 

.000  631 1154 

1578 

2  490  084 

3  92'J  352552 

39.724  01-1 

11.642  2164 

.000  633  7136 

1579 

2  493  241 

3  936  827  539 

39.736  6329 

11.611  07.-.1 

.000  633  3122 

1580 

2  196  400 

3  944  312  000 

39.749  21:38 

11.047  1329 

.000  632  9114 

1581 

2  199  561 

3  95 1805  941 

39.761  7907 

11.049  5895 

.000  632  5111 

1582 

2  502  724 

3  959  309  368 

39.774  3636 

11.6520452 

.000  632  1113 

1583 

2  505  889 

3  966  822  287 

39.786  9:: 25 

11.654  4998 

.000  6:317119 

1584 

2  509  056 

3  974  314  704 

39.799  4976 

11.656  9534 

.000  631  3131 

1585 

2  ".12  225 

3  981  876  025 

39.812  0585 

11.659  4059 

.000  630  9148 

1586 

2  515  396 

3  989  418  056 

39.824  6155 

11.6618574 

.000  630  5170 

1587 

2  518  569 

3  996  969  003 

39.837  1686 

11.004  3079 

.000  630  1197 

1588 

2  .".21  744 

4  004  529  472 

39.849  7177 

11.000  7."  71 

.000  629  7229 

1589 

2  524  921 

4  012  099  469 

39.862  2628 

11.669  2058 

.000  629  3266 

1590 

2  528  100 

4  014  679  000 

39.874  8040 

11.6716532 

.000  628  9308 

1591 

2  531  281 

4  027  268  071 

39.887  3413 

11.674  0996 

.000  628  5355 

1592 

2  534  464 

4  034  866  688 

39.899  8747 

11.076  5419 

.000  628  1407 

1593 

2  537  649 

4  042  474  857 

39.912  4041 

11.078  9892 

.000  627  7464 

1594 

2  540  836 

4  050  092  584 

39.924  9295 

1L681  4325 

.000  627  3526 

1595 

2544025 

4  057  719  875 

39.937  4511 

11.683  8748 

.000  626  9592 

15% 

21 ">  17  216 

4  065  356  736 

39.949  9687 

11.686  3161 

.000  626  5664 

1597 

2  5  50  409 

4  073  003  173 

39.962  4*24 

11.688  7563 

.000  626  1741 

1598 

2  553  604 

1  080659192 

39.974  9922 

11.691 1955 

.000  625  7822 

1599 

2  556  801 

4  088  324  799 

39.987  4980 

11.693  6337 

.000  625  3909 

1600 

2  560  000 

4  096  000  000 

40.000  0000 

11.696  0709 

.000  625  0000 

The  use  of  the  table  of  powers  and  roots  may  be  extended  far  beyond 
its  apparent  limits  by  the  observance  of  the  following  rules: 

Remembering  that  the  extraction  of  the  square  root  of  a  number  is 
simply  the  separating  it  into  two  equal  factors,  we  have :  to  extract  the 
square  root  of  any  whole  number  and  decimal,  when  the  whole  number  is 
within  the  limits  of  the  table,  simply  find  the  square  root  of  the  whole 
number  in  the  table  and  divide  the  Viven  number  and  decimal  by  this 
root.  The  quotient  will  l>e  another  factor,  very  nearly  equal  to  the  required 
root.  Add  the  divisor  and  the  quotient  together  and  divide  by  two,  and 
the  result  will  t>e  the  true  root  to  a  very  close  degree  of  approximation. 
These  tables,  together  with  those  <.f  Sletric  System  and  Logarithms  have 
been  taken  by  permission  from  Suplee's  M  Reference  Book." 


552 


Logarithms. 


LOGARITHMS. 

There  are  four  fundamental  rules  for  operations  with  powers : 

am  ,  an  —  am  +  «. 

That  is,  the  product  of  any  two  powers  of  a  number  is  equal  to  the  num- 
ber raised  to  a  power  whose  exponent  is  the  sum  of  the  exponents  of  the 
two  factors. 


an 


Or,  the  quotient  of  two  powers  is  equal  to  the  number  raised  to  a  power 
whose  exponent  is  the  difference  of  the  exponents  of  divisor  and  dividend. 


(any 


amn. 


Or,  any  power  may  be  raised  to  a  higher  power  by  multiplying  the  two 
exponents. 

V  am  =  a  n  . 

Or,  any  root  of  any  power  may  be  extracted  by  dividing  the  exponent  by 
the  index  of  the  root. 

If  we  take  any  number,  such  as  2,  and  use  it  as  the  base  of  a  geometrf- 
cal  series,  we  will  see  that  the  exponents  form  an  arithmetical  series. 
Thus,  the  exponent  of  1  =  0,  of  2  =  1,  of  4  =  2,  of  8  =  3,  etc. ;  or,  proceed- 
ing, we  may  arrange  the  following  little  table : 


Powers. 

Exponents. 

Powers. 

Exponents. 

Powers. 

Exponents. 

1 

0 

1024 

10 

1048576 

20 

2 

1 

2048 

11 

2097152 

21 

4 

2 

4096 

12 

4194304 

22 

8 

3 

8192 

13 

8388608 

23 

16 

4 

16384 

14 

16777216 

24 

32 

5 

32768 

15 

64 

6 

65536 

16 

128 

7 

131072 

17 

256 

8 

262144 

18 

512 

9 

524288 

19 

Suppose  now  we  wish  to  multiply  128  by  512,  we  see  that  128  =  27  and 
512  =  29;  hence,  128  X  512  =  2^9  =  2",  and  in  the  table,  opposite  the 
exponent  16,  we  find  the  power  65536,  which  is  the  product  of  the  two 
factors,  obtained  by  the  simple  addition  of  the  exponents. 


Again, 


^  =  ^-  =  29-7  =  22  =  4. 
128       2? 


To  raise  a  number  to  a  power,  such  as  16  to  the  fifth  power,  we  have 
16  =  2*  and  (2*)&  =  2*>  =  1048576. 

Again,  the  seventh  root  of  2097152  is  formed  as  follows : 

2097152  =  22i  and  {/  221  =  2"  =  23  =  8. 

In  the  small  table  of  the  powers  of  2  given  above  there  are  many  gaps, 
because  only  those  powers  which  have  whole  exponents  are  given.  For  all 
the  numbers  between  16  and  32,  for  example,  the  exponents  will  be  deci- 
mals, and  will  be  greater  than  4  and  less  than  5,  etc.  In  practice,  the  base 
used  is  not  2,  but  10,  and  all  the  intermediate  exponents  have  been  com- 
puted to  many  decimals,  these  forming  a  table  of  logarithms. 


Logarithms.  553 


Table  of  Logarithms  of  Numbers. 

rages  82  to  104  give  the  mantissas,  or  decimal  portions  of  the  logarithms, 
of  all  whole  numbers  from  1  to  10009.  The  characteristics,  or  whole  num- 
bers, which,  with  these  decimals,  form  the  complete  logarithms,  are  found 
as  follows : 

The  logarithm  of  1  =  0,  of  10  =  1,  of  100  =  2,  of  1000  =  3,  etc. ;  hence, 
the  logarithm  of  any  number  between  1  < hj  and  1000  must  lie  between  2  and 
3,  ami  be  greater  than  2  and  l<-ss  than  3,  and  so  for  any  number.  There- 
fore we  have  the  rule  that  the  whole  portion  of  a  loparithm  of  any  num- 
ber is  one  less  than  there  are  figures  in  the  numlier.  The  decimal  portion 
for  any  number  below  10009  is  taken  directly  from  the  table.     Thus, 

log.  365  =  2.56229, 

the  decimal  portion,  56229,  being  found  directly  opposite  365  in  the  table, 
and  the  whole  portion  t>eing  2,  or  1  less  than  the  number  of  places  in  365. 
In  like  manner  we  have 

log.  36.5    =  1.56229, 
log.    3.65  =  0.56229. 

The  mantissa,  or  decimal  portion,  is  always  positive,  but  the  character- 
istic is  negative  when  the  number  is  less  than  unity.     Thus, 

log.  0.365  =1.56229, 
log.  0.0365  ="2.56229, 
log.  0.00365=5.56229, 

the  minus  being  placed  nrrr  the  characteristic  to  show  that  it  applies  to 
that  portion  only,  and  not  to  the  mantissa. 

If  the  given  number  has  more  than  three  places,  the  mantissa  is  found 
in  the  body  of  the  table.  Thus,  the  logarithm  of  1873  =  3.27254.  the  figures 
0.27  being  found  opposite  187,  and  the  254  on  the  same  horizontal  line 
under  3. 

If  the  last  three  figures  of  the  mantissa  are  preceded  by  an  asterisk,  the 
first  two  figures  are  to  be  taken  from  the  next  line  below,  in  the  first 
column.    Thus, 

log.  3S97  =  3.59073, 

in  which,  opposite  389,  we  find  58,  and  then,  passing  on  under  7,  we  find 
*073,  the  asterisk  indicating  that  we  are  to  go  one  line  below,  taking  out 
59,  not  58,  for  the  first  two  figures  of  the  mantissa,  giving  us  0.59073,  as 
above. 

The  table,  as  will  be  seen,  enables  the  logarithm  of  any  number  of  jovr 
places  to  be  taken  out  at  once.  If  the  number  of  which  the  logarithm  is 
required  has  more  than  four  places,  the  logarithm  can  be  found  from  the 
table,  as  follows : 

In  the  column  at  the  extreme  right  of  each  page,  under  the  heading 
P.  P.  (Proportional  Parts),  will  be  found  in  the  black  figures  the  differences 
between  any  logarithm  and  the  next  succeeding  logarithm  for  the  adjoin- 
ing portions  of  the  table.  The  smaller  figures  in  the  same  column  form 
little  multiplication  tables,  in  which  these  differences  are  multiplied  bv 
0.1.  0.2.  0.3,  etc. 

The  use  of  these  proportional  parts  and  their  decimal  parts  is  best 
shown  by  actual  example.  Suppose  it  is  desired  to  find  the  logarithm  of 
18702.  Opposite  187  and  under  0  in  the  table  we  find  the  mantissa,  0.271M. 
The  proportional  part,  or  difference  at  this  point  between  one  logarithm 
and  the  next,  is  23,  or,  in  other  words,  there  is  a  difference  of  23  between 
the  last  two  figures  of  the  logarithm  of  1870  and  1871.  For  0.1  difference 
in  the  number,  the  difference  in  the  logarithms  would  be  2.3 ;  for  0.2,  it 
would  be  4.6,  etc.,  as  shown  in  the  small  table  under  23  in  tbe  column 
P.  P.  Fur  2  points  additional,  therefore,  we  simply  add  4.6  to  the  loga- 
rithm of  1870,  and  we  have  the  logarithm  of  18702.    Thus, 

log.  1870     =  0.27184 
p.  p.  for  2  =  4.6 

log.  18702  =  4.271886,  or 
4.27189 


554  Logarithms. 


Again,  let  it  be  required  to  find  the  logarithm  of  35.797. 

log.  35.79   =  1.55376      p.  p.  =  12 
p.  p.  for  7  =  8.4 

log.  35.797  =  1.553844 

If  the  given  number  has  six  or  more  figures  the  method  is  the  same, 
except  that  the  proportional  part  is  reduced  one-tenth  for  each  additional 
figure.    Thus,  the  logarithm  of  3725.96  is  found  as  follows  : 

log.  3725      =  3.57113        p.  p.  =  11 
p.  p.  for  9    =  9.9 

p.  p.  for  6    =  0.66 

log.  3725.96  =  3.5712356,  or  3.57124 

The  operation  of  finding  the  number  corresponding  to  a  given  loga- 
rithm is  the  reverse  of  the  preceding.  Thus,  the  number  corresponding  to 
the  logarithm  2.73924  is  found  as  follows  : 

In  the  table  the  next  smaller  logarithm  is 

73918,  and  its  number  =  584500 

The  given  log.  =  73924 

and  the  difference  =6 
The  nearest  difference  in  the  table  =  5.6  =  corresponding  to  7 

Subtracting      0.4      corresponding  to  5 

Hence,  the  number  is      584575 
Since  the  characteristic  =  2,  there  must  be  one  more  place 
before  the  decimal  point ;  hence, 

log.  2.73924  =  num.     584.575 


Logarithms  of  Numbers. 


555 


Num.    J 00  to   139.      Log.  000  to  145. 


N 

L 

0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

100 

00 

000 

043 

087 

130 

17:; 

217 

260 

303 

846 

44 

43 

101 

432 

175 

618 

561 

604 

647 

689 

732 

775  M  7 

i   *  * 

t  1 
8.6 

102 

860 

903 

945 

988  *030 

•072 

*115 

*157  *199  *242 

1 
2 

1. 1 
8.8 

103 

01 

284 

326 

::c.s 

410 

452 

494 

536 

578 

620  662 

:; 

13.2 

12.9 

104 

703 

715 

787 

828 

870 

912 

953 

995  *036  *078 

I 

5 

17.6 
22.0 

17.2 
21.5 

105 

02 

119 

160 

202 

243 

284 

325 

366 

407 

449  400 

6 

7 
8 

26.4 

30.8 

:>.:<:2 

25.8 
30.1 
34.4 

IOC 

531 

572 

612 

653 

694 

785 

776 

816 

857  898 

107 

938 

979  *019  *060  *100 

*141  *181 

*222 

•262  *302 

9 

39.6 

38.7 

108 

03 

342 

383 

423 

463 

503 

543 

583 

623 

663  703 

*  ■>   *  ^ 

109 

743 

782 

822 

862 

902 

941 

981  *021  *060  *100 

42 

*i 

no 

01 

139 

179 

218 

258 

297 

336 

376 

11". 

454  493 

1 
2 

4.2 

8.4 

4.1 

8.2 

in 

532 

571 

610 

650 

689 

727 

766 

805 

844 

3 

12.6 

12.3 

112 

922 

961 

999  *038  *077 

*115 

*154  *192 

•231  *269 

4 
5 
6 

16.8 
21.0 
25.2 

16.4 
20.5 
24.6 

U3 

05 

::u> 

346 

385 

423 

461 

500 

538 

576 

61 1  652 

114 

690 

729 

767 

805 

843 

881 

918 

956 

994  *032 

7 

29.4 

28.7 

115 

06 

070 

108 

145 

183 

221 

258 

2% 

333 

371  408 

8 
9 

33.6 
37.8 

32.8 
36.9 

116 

446 

483 

521 

558 

595 

633 

670 

707 

744  781 

JA     -.  ,  . 

117 

819 

856 

893 

930 

967 

*004  *041  *078  *115  *151 

4U 

«jy 

118 

07 

188 

225 

262 

298 

335 

372 

408 

4  15 

482  51S 

1 

4.0 

3.9 

119 

555 

591 

628 

664 

700 

737 

773 

809 

846  882 

2 
3 

8.0 
12.0 

7.8 
11.7 

120 

918 

954 

990  *027 

•063 

*099  *135 

*171  *207  *243 

4 
5 
6 

16.0 
20.0 
24.0 

15.6 
19.5 
23.4 

121 

08 

279 

314 

350 

3S6 

422 

458 

493 

529 

565  600 

122 

636 

672 

707 

743 

778 

814 

849 

SS-l 

920  955 

7 

28.0 

27.3 

123 

991  *026  *061  *096  *132 

•167 

•202  *237 

*272  *307 

s 

32.0 

31.2 
35.1 

124 

09 

342 

377 

412 

447 

482 

517 

552 

587 

621  656 

9  |OD.U 

125 

691 

726 

760 

795 

830 

864 

899 

934 

968  *003 

38 

37 

126 

10 

037 

072 

106 

140 

175 

209 

243 

278 

312  346 

1 

3.8 

3.7 

127 
128 

380 

721 

415 
755 

449 
789 

483 
823 

517 
857 

551 
890 

585 
924 

619 
958 

653  687 
992  •025 

2 
3 
4 

7.6 
11.4 
15.2 

7.4 
11.1 
14.8 

129 

11 

059 

093 

126 

160 

193 

227 

261 

294 

327  361 

5 

19.0 

18.5 

130 

128 

161 

[94 

528 

561 

594 

661  694 

6 

7 

22.8 
26.6 

22.2 
25.9 

131 

727 

760 

793 

826 

860 

893 

926 

959 

992  *024 

8 
9 

30.4 
34.2 

29.6 

132 

12 

057 

090 

123 

166 

189 

222 

254 

287 

320  352 

33.3 

133 

385 

418 

450 

483 

516 

548 

581 

613 

646  678 

36 

35 

134 

710 

713 

775 

MIS 

840 

872 

905 

937 

969  *001 

1 

3.6 

3.5 

136 

136 

13 

033 
35  i 

066 
386 

098 
418 

130 
450 

162 

481 

194 
513 

226 
545 

258 
577 

290  322 
609  640 

2 
3 

1 

7.2 
10.8 
14.4 

7.0 
10.5 
14.0 

137 

672 

704 

735 

767 

799 

830 

862 

893 

925  956 

5 

18.0 

17.5 

138 

130 

14 

988  *019  *051  *082  *114 
301  333  364  395  126 

*1  15  *176  *208  *289  *270 
157  ISO  520  551  582 

6 

7 
8 

21.6 
25.2 
28.8 

21.0 

21.5 

28.0 

140 

613 

644 

675 

706 

737 

768 

799 

820 

860  891 

9 

32.4 

31.6 

N 

L 

0 

1 

2 

3 

4 

s 

6 

7 

8   9 

P.  P 

556 


Logarithms  of  Numbers. 


Num.   140  to  179.     Log.   146  to  255. 


N 

140 

141 
142 
143 
144 

145 
146 
147 
148 
149 

150 

151 
152 
153 
154 

155 
156 
157 
158 
159 

160 

161 
162 
163 
164 

165 
166 
167 
168 
169 

170 

171 
172 
173 
174 

175 
176 

177 
178 
179 

180 

N 


L01234  56789 


14 


15 


16 


613  644  675  706  737 

922  953  983  *014  *045 

229  259  290  320  351 

534  564  594  625  655 

836  866  897  927  957 


137  167  197  227  256 

435  465  495  524  554 

732  761  791  820  850 

17  026  056  085  114  143 
319  348  377  406  435 

609  638  667  696  725 

898  926  955  984  *013 

18  184  213  241  270  298 
469  498  526  554  583 
752  780  808  837  865 

19  033  061  089  117  145 
312  340  368  396  424 
590  618  645  673  700 
866  893  921  948  976 

20  140  167  194  222  249 

412  439  466  493  520 

683  710  737  763  790 

952  978  *005  *032  *059 

21  219  245  272  299  325 
484  511  537  564  590 

748  775  801  827  854 

22  011  037  063  089  115 
272  298  324  350  376 
531  557  583  608  634 
789  814  840  866  891 

23  045  070  096  121  147 
300  325  350  376  401 
553  578  603  629  654 
805  830  855  880  905 

24  055  080  105  130  155 

304  329  353  378  403 

551  576  601  625  650 

797  822  846  871  895 

25  042  066  091  115  139 
285  310  334  358  382 

527  551  575  600  624 

L   0  1  2  3  4 


768  799  829  860  891 

*076  *106  *137  *168  *198 

381  412  442  473  503 

685  715  746  776  806 

987  *017  *047  *077  *107 

286  316  346  376  406 

584  613  643  673  702 

879  909  938  967  997 
173  202  231  260  289 
464  493  522  551  580 

754  782  811  840  869 

*041  *070  *099  *127  *156 

327  355  384  412  441 

611  639  667  696  724 

893  921  949  977  *005 

173  201  229  257  285 

451  479  507  535  562 

728  756  783  811  838 

*003  *030  *058  *085  *112 

276  303  330  358  385 

548  575  602  629  656 

817  844  871  898  925 

*085  *112  *139  *165  *192 

352  378  405  431  458 

617  643  669  696  722 

880  906  932  958  985 
141  167  194  220  246 
401  427  453  479  505 
660  686  712  737  763 
917  943  968  994  *019 

172  198  223  249  274 

426  452  477  502  528 

679  704  729  754  779 

930  955  980  *005  *030 

180  204  229  254  279 

428  452  477  502  527 

674  699  724  748  773 

920  944  969  993  *018 

164  188  212  237  261 

406  431  455  479  503 

648  672  696  720  744 


P.  P. 


34 

33 

1 

3.4 

3.3 

2 

6.8 

6.6 

3 

10.2 

9.9 

4 

13.6 

13.2 

5 

17.0 

16.5 

6 

20.4 

19.8 

7 

23.8 

23.1 

8 

27.2 

26.4 

9 

30.6 

29.7 

32 

31 

1 

3.2 

3.1 

2 

6.4 

6.2 

3 

9.6 

9.3 

4 

12.8 

12.4 

5 

16.0 

15.5 

6 

19.2 

18.6 

7 

22.4 

21.7 

8 

25.6 

24.8 

9 

28.8 

27.9 

30 

29 

1 

3.0 

2.9 

2 

6.0 

5.8 

3 

9.0 

8.7 

4 

12.0 

11.6 

5 

15.0 

14.5 

6 

18.0 

17.4 

7 

21.0 

20.3 

8 

24.0 

23.2 

9 

27.0 

26.1 

28 

27 

1 

2.8 

2.7 

2 

5.6 

5.4 

3 

8.4 

8.1 

4 

11.2 

10.8 

5 

14.0 

13.5 

6 

16.8 

16.2 

7 

19.6 

18.9 

8 

22.4 

21.6 

9 

25.2 

24.3 

26 

25 

1 

2.6 

2.5 

2 

5.2 

5.0 

3 

7.8 

7.5 

4 

10.4 

10.0 

5 

13.0 

12.5 

6 

15.6 

15.0 

7 

18.2 

17.5 

8 

20.8 

20.0 

9 

23.4 

22.5 

P.  p. 


Logarithms   of  Nfmrers. 


bbl 


Num 

,  180  to 

219. 

Log. 

255 

to  342. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P.  P. 

180 

2.'.   527 

551 

575 

600 

624 

648 

672 

6%  720  711 

24 

181 

768 

792 

816 

840 

864 

888 

912 

959  983 

1 
2 

2.1 
1.8 

182 

26   007 

031 

066 

079 

102 

126 

150 

171  196  2-21 

183 

245 

269 

293 

316 

340 

364 

387 

411  435  458 

3 

7.2 

181 

182 

505 

529 

553 

576 

600 

623 

617  670  694 

4 
5 

9.6 
12.0 

185 

186 

717 
951 

711 

764  788  811 
988  •021  *045 

834  838  881  905  928 
*068  *091  *114  *138  *161 

6 

7 
K 

14.4 

16.8 
192 

187 

27   1  - 1 

207 

231 

254 

277 

300 

346  370  393 

9 

21.6 

1- 

416 

439 

462 

K5 

508 

531 

5-54 

577  600  623 

23 

189 

646 

669 

692 

715 

738 

761 

784 

807  830  852 

190 

875 

s-.K 

921 

944 

967 

989  *012  *035  *058  *081 

1 
2 

2.3 
4.6 

191 

28   103 

126 

149 

171 

194 

•217 

240 

262  285  307 

3 

6.9 

192 

330 

375 

398 

421 

443 

466 

488  511  533 

4 

5 
6 

9.2 

11.5 

1  13.8 

556 

578 

601 

623 

646 

668 

691 

713  735  758 

194 

780 

803 

- 

-17 

870 

892 

914 

937  959  981 

7 

16.1 
18.4 

195 

29   003 

026 

048 

070 

092 

115 

137 

181  203 

9 

20.7 

196 

226 

24  S 

270 

292 

314 

336 

358 

380  403  125 

22 

197 

447 

469 

491 

513 

535 

557 

579 

601  623  645 

198 

667 

,>N 

710 

732 

754 

77'', 

798 

820  842  863 

1 

2.2 

199 

38 

907 

929 

951 

973 

994  *016  *038  *060  *081 

o 

o 

4.4 
6.6 

200 

30   103 

125 

146 

168 

190 

211 

255  276  298 

4 
5 
6 

8.8 
11.0 
13.2 

201 

320 

341 

363 

- 

406 

428 

449 

471  492  514 

202 

535 

J 

578 

600 

621 

643 

664 

685  707  728 

7 

15.4 

203 

750 

771 

792 

814 

835 

- 

878 

899  920  942 

8 

Q 

17.6 

204 

963 

984  *006  *027  *048 

*069  *091  *112  *133  *154 

y  I?. o 

205 

31   175 

197 

218 

239 

260 

281 

302 

323  345  366 

21 

206 

387 

408 

429 

4-50 

471 

492 

513 

534  555  576 

1 

2.1 

207 

597 

618 

639 

660 

681 

702 

723 

744  765  785 

2 

3 
4 

4.2 
6.3 

8.4 

- 

806 

327 

848 

869 

890 

911 

931 

952  973  994 

209 

32   015 

077 

098 

118 

139 

160  181  201 

5 
6 

10.5 
12.6 

210 

222 

243 

263 

284 

305 

325 

346 

366  387  408 

7 

14.7 

211 

428 

449 

469 

490 

510 

531 

552 

572  593  613 

8 

Q 

16.8 

1C  (\ 

212 

634 

•  '•! 

675 

695 

715 

736 

756 

777  797  818 

IO.S 

213 

838 

858 

899 

919 

940 

960 

980  *001  *021 

20 

19 

214 

041 

082 

10-2 

122 

1  43 

163 

183  203 

1 

2.0 

1.9 

•21:. 

241 

264 

284 

304 

325 

345 

365 

385  405  425 

2 
8 

4 

4.0 
6.0 
8.0 

3.8 
5.7 

7.6 

216 

(45 

465 

486 

506 

526 

.546 

566 

586  606  626 

217 

646 

666 

686 

706 

72-; 

746 

766 

786  806  826 

5  1 

0.0 

9.5 

218 

B46 

866 

885 

905 

925 

945 

965 

985  *005  *025 

6  1 

"  1 

-  1 

2.0 
1.0 

6.0 

11.4 
13.3 

15.2 

219 

Oil 

064 

084 

104 

124 

143 

163 

183  203  2-23 

220 

282 

301 

321 

341 

361 

380  400  420 

9  1 

8.0 

17.1 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P.  P. 

558 


Logarithms  of  Numbers. 


Sum 

.  220  to 

259. 

Log.  342  to  414. 

N 

L   0 

1 

2 

3 

4 

5   6   7 

8   9 

P.  P. 

220 

34   242 

262 

282 

301 

321 

341  361  3S0 

400  420 

221 

439 

459 

479 

498 

518 

537  557  577 

596  616 

20 

222 

635 

655 

674 

694 

713 

733  753  772 

792  811 

1 

2.0 

223 

830 

850 

869 

889 

908 

928  947  967 

986  *005 

2 

4.0 

224 

35   025 

044 

064 

083 

102 

122  141  160 

180  199 

3 
4 

6.0 
8.0 

225 

218 

238 

257 

276 

295 

315  334  353 

372  392 

5 
6 

7 

10.0 
12.0 
14.0 

226 

411 

430 

449 

468 

488 

507  526  545 

564  583 

227 

603 

622 

641 

660 

679 

698  717  736 

755  774 

8 

16.0 

228 

793 

813 

832 

851 

870 

889  908  927 

946  965 

9 

18.0 

229 

984  *003  *021  *040  *059 

*078  *097  *116  *135  *154 

230 

36   173 

192 

211 

229 

248 

267  286  305 

324  342 

19 

231 

361 

380 

399 

418 

436 

455  474  493 

511  530 

232 

549 

568 

586 

605 

624 

642  661  680 

698  717 

1 

1.9 

233 

736 

754 

773 

791 

810 

829  847  866 

884  903 

2 
3 
4 

3.8 
5.7 
7.6 

234 

922 

940 

959 

977 

996 

*014  *033  *051  *070  *088 

235 

37   107 

125 

144 

162 

181 

199  218  236 

254  273 

5 
6 

9.5 
11.4 

236 

291 

310 

328 

346 

365 

38   401  420 

438  457 

7 

13.3 

237 

475 

493 

511 

530 

548 

566  5   603 

621  639 

8 
9 

15.2 
17.1 

238 

658 

676 

694 

712 

731 

749  767  785 

803  822 

239 

840 

858 

876 

894 

912 

931  949  967 

985  *003 

240 

38   021 

039 

057 

075 

093 

112  130  148 

166  184 

241 

202 

220 

238 

256 

274 

292  310  328 

346  364 

18 

242 

382 

399 

417 

435 

453 

471  489  507 

525  543 

243 

561 

578 

596 

614 

632 

650  668  686 

703  721 

1 

1.8 

244 

739 

757 

775 

792 

810 

828  846  863 

881  899 

2 
3 

3.6 
5.4 

245 

917 

934 

952 

970 

987 

*005  *023  *041 

*058  *076 

4 
5 

7.2 

9.0 

10.8 

246 

39   094 

111 

129 

146 

164 

182  199  217 

235  252 

6 

247 

270 

287 

305 

322 

340 

358  375  393 

410  428 

7 

12.6 

248 

445 

463 

480 

498 

515 

533  550  568 

585  602 

8 
9 

14.4 

249 

620 

637 

655 

672 

690 

707  724  742 

759  777 

250 

794 

811 

829 

846 

863 

881  898  915 

933  950 

251 

967 

985 

*002  *019  *037 

*054  *071  *088  *106  *123 

252 

40   140 

157 

175 

192 

209 

226  243  261 

278  295 

253 

312 

329 

346 

364 

381 

398  415  432 

449  466 

17 

2,54 

483 

500 

518 

535 

552 

569  586  603 

620  637 

1 

1.7 

255 

654 

671 

688 

705 

722 

739  756  773 

790  807 

2 
3 

3.4 
5.1 

256 

824 

841 

858 

875 

892 

909  926  943 

960  976 

4 

6.8 

257 

993  *010  *027  *044  *0fil 

*078  *095  *111  *128  *145 

5 
6 
7 

8.5 
10.2 
11.9 

258 

41   162 

179 

196 

212 

229 

246  263  280 

296  313 

259 

330 

347 

363 

380 

397 

414  430  447 

464  481 

8 
9 

13.6 
15.3 

260 

497 

514 

531 

547 

564 

581  597  614 

631  647 

N 

L   0 

1 

2 

3 

4 

5   6   7 

8   9 

P.  P. 

Logarithms  of  Numbers. 


559 


Num.  260  to  299.     Log.  414  to  476. 


N 

L    0 

1 

2 

3 

4 

5 

6 

7   8   9 

P.  P. 

260 

41   497 

514 

531 

547 

564 

581 

597 

614  631  647 

261 

664 

681 

697 

714 

731 

747 

764 

7-n  797  814 

262 

830 

847 

880 

8% 

929 

946  963  979 

263 

9%  *012 

*029  *045 

•062 

*078  *095 

*111  *127  144 

264 

42   160 

177 

193 

210 

226 

243 

259 

275  292  308 

17 

265 

325 

341 

357 

374 

390 

406 

423 

439  455  172 

1 
2 

1.7 
3.4 

266 

488 

504 

521 

537 

553 

570 

586 

602  619  635 

267 

651 

667 

684 

700 

716 

732 

749 

765  781  797 

3 

5.1 

268 

813 

830 

846 

-2 

878 

894 

911 

927  943  959 

4 
5 
6 

6.8 

v5 
10.2 

269 

975 

991 

*008  *024  *040 

•056  *072 

*088  *104  *120 

270 

43   136 

152 

169 

188 

201 

217 

. 

249  265  281 

7 
8 

11.9 
13.6 

271 

297 

313 

329 

345 

361 

377 

393 

409  425  441 

9 

15.3 

272 

457 

473 

489 

505 

521 

537 

553 

569  584  600 

273 

616 

632 

648 

664 

680 

696 

712 

727  713  759 

274 

775 

791 

807 

823 

838 

854 

870 

886  902  917 

n 

933 

949 

965 

981 

996 

•012 

•028  *044  *059  *076 

271 

44   091 

107 

122 

138 

154 

170 

185 

201  217  232 

16 

277 

248 

264 

279 

295 

311 

326 

342 

358  373  389 

278 

404 

420 

436 

451 

467 

483 

498 

514  529  545 

1 

1.6 

279 

560 

576 

592 

607 

623 

638 

654 

669  6*5  700 

2 
3 

3.2 

4.8 

280 

716 

731 

747 

762 

778 

793 

809 

824  840  855 

4 

6.4 
8.0 

281 

871 

886 

902 

917 

932 

948 

963 

979  994  *010 

6 

9.6 

282 

15   025 

040 

056 

071 

Usr, 

102 

117 

133  148  163 

7 

11.2 

179 

194 

209 

225 

240 

255 

271 

286  301  317 

8 
9 

12.8 

14  4 

284 

332 

347 

362 

378 

393 

406 

423 

439  454  469 

57    ....... 

285 

484 

500 

515 

530 

545 

561 

576 

591  606  621 

'J-. 

637 

652 

667 

-- 

697 

712 

728 

743  758  773 

287 

788 

803 

818 

834 

849 

-'•,4 

B79 

894  909  924 

288 

939 

954 

969 

984  *000 

*015  *030  *045  *060  *075 

2*9 

4*   090 

105 

120 

135 

150 

165 

ISO 

195  210  225 

IS 

290 

240 

255 

270 

285 

300 

315 

330 

345  359  374 

1 

1.5 

r.  n 

291 
292 

389 
538 

404 
553 

419 
568 

434 
583 

449 

598 

4tV4 
613 

479 
627 

494  509  523 
642  657  672 

1 

4 

3.0 

1.5 

6.0 

293 

702 

716 

731 

746 

761 

776 

790  805  -- 

5 

7.5 

294 

• 

850 

864 

994 

909 

923 

938  953  967 

6 

7 

9.0 
10.5 

295 

- 

997 

•012 

*026  *041 

•056  *070  *085  *100  *111 

8 
9 

12.0 

13  ."S 

296 

17   129 

111 

159 

17:: 

188 

202 

217 

232  216  261 

•j  |  . 

297 

276 

290 

305 

319 

334 

349 

378  392  107 

422 

436 

151 

165 

(80 

494 

509 

524  538  553 

299 

567 

- 

611 

640 

654 

669  683  698 

300 

712 

727 

711 

756 

770 

784 

799 

813  828  842 

N 


P.  P. 


560 


Logarithms  of  Numbers. 


Num.  300  to  339.     Log.  477  to  531. 


N 

L   0 

1 

2 

3 

4 

5   6   7 

8   9 

P.  P. 

300 

47   712 

727 

741 

756 

770 

784  799  813 

828  842 

301 

857 

871 

885 

900 

914 

929  943  958 

972  986 

302 

48   001 

015 

029 

044 

058 

073  087  101 

116  130 

303 

144 

159 

173 

187 

202 

216  230  244 

259  273 

304 

287 

302 

316 

330 

344 

359  373  387 

401  416 

14 

305 

430 

444 

458 

473 

487 

501  515  530 

544  558 

1   ■<  * 

306 

572 

586 

601 

615 

629 

643  657  671 

686  700 

l 

2 

2.8 

307 

714 

728 

742 

756 

770 

785  799  813 

827  841 

3 

4.2 

308 

855 

869 

883 

897 

911 

926  940  954 

968  982 

4 
5 
6 

5.6 
7.0 

8.4 

309 

996  *010 

*024  *038  *052 

*066  *080  *094  *108  *122 

310 

49   136 

150 

164 

178 

192 

206  220  234 

248  262 

7 
8 

9.8 
11.2 

311 

276 

290 

304 

318 

332 

346  360  374 

388  402 

9 

12.6 

312 

415 

429 

443 

457 

471 

485  499  513 

527  541 

313 

554 

568 

582 

596 

610 

624  638  651 

665  679 

314 

693 

707 

721 

734 

748 

762  776  790 

803  817 

315 

831 

845 

859 

872 

886 

900  914  927 

941  955 

316 

969 

982 

996  *010  *024 

*037  *051  *065  *079  *092 

13 

317 

50   106 

120 

133 

147 

161 

174  188  202 

215  229 

318 

243 

256 

270 

284 

297 

311  325  338 

352  365 

1 

1.3 

319 

379 

393 

406 

420 

433 

447  461  474 

488  501 

2 
3 

2.6 
3.9 

320 

515 

529 

542 

556 

569 

583  596  610 

623  637 

4 
5 
6 

5.2 
6.5 

7.8 

321 

651 

664 

678 

691 

705 

718  732  745 

759  772 

322 

786 

799 

813 

826 

840 

853  866  880 

893  907 

7 

9.1 

323 

920 

934 

947 

961 

974 

987  *001  *014  *028  *041 

8 
9 

10.4 
11.7 

324 

51   055 

068 

081 

095 

108 

121  135  148 

162  175 

325 

188 

202 

215 

228 

242 

255  268  282 

295  308 

326 

322 

335 

348 

362 

375 

388  402  415 

428  441 

327 

455 

468 

481 

495 

508 

521  534  548 

561  574 

328 

587 

601 

614 

637 

640 

654  667  680 

693  706 

329 

720 

733 

746 

759 

772 

786  799  812 

825  838 

12 

330 

851 

865 

878 

891 

904 

917  930  943 

957  970 

1 

1.2 

331 

983 

996  *009  *022  *035 

*048  *061  *075 

*088  *101 

2 
3 
4 

2.4 
3.6 

4.8 

332 

52   114 

127 

140 

153 

166 

179  192  205 

218  231 

333 

244 

257 

270 

284 

297 

310  323  336 

349  362 

5 

6.0 

334 

375 

388 

401 

414 

427 

440  453  466 

479  492 

6 

7 

7.2 
8.4 

335 

504 

517 

530 

543 

556 

569  582  595 

608  621 

8 
9 

9.6 
10.8 

336 

"  634 

647 

660 

673 

686 

699  711  724 

737  750 

337 

763 

776 

789 

802 

815 

827  840  853 

866  879 

338 

892 

905 

917 

930 

943 

956  969  982 

994  *007 

339 

53   020 

033 

046 

058 

071 

084  097  110 

122  135 

340 

148 

161 

173 

186 

199 

212  224  237 

250  263 

N 

L   0 

1 

2 

3 

4 

5   6   7 

8   9 

P.  P. 

Logarithms  of  Numbers. 


m 


Num.  340  to  379.     Log.  531   to  579. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P 

,  P. 

340 

53   148 

161 

173 

186 

199 

212 

224 

250 

341 

275 

288 

301 

314 

326 

339 

352 

; 

377  390 

342 

403 

415 

441 

466 

47y 

491 

504  517 

343 

529 

542 

555 

567 

580 

593 

605 

618 

631  643 

344 

656 

668 

681 

694 

706 

719 

732 

744 

757  769 

13 

845 

782 

794 

807 

820 

832 

845 

857 

870 

882  895 

1 
2 

1.3 

2.6 

340 

920 

933 

945 

958 

970 

983 

995  *008  *020 

347 

54   033 

045 

058 

070 

- 

095 

108 

120 

133  145 

3 

3.9 

348 

158 

170 

183 

195 

208 

220 

233 

245 

258  270 

4 

5 
6 

5.2 
6.5 
7.8 

349 

283 

295 

307 

320 

332 

345 

357 

370 

382  394 

350 

407 

419 

432 

444 

456 

469 

481 

494 

506  518 

7 
8 

9.1 
10.4 

351 

531 

543 

555 

568 

5S0 

593 

605 

617 

630  642 

9 

11.7 

352 

654 

667 

679 

691 

704 

716 

728 

741 

753  765 

353 

777 

790 

802 

814 

827 

839 

851 

864 

876  888 

354 

900 

913 

925 

937 

949 

962 

974 

9S6 

998  *011 

355 

55   023 

035 

047 

060 

072 

084 

0% 

108 

121  133 

356 

145 

157 

169 

182 

194 

206 

218 

230 

242  255 

12 

357 

267 

279 

291 

303 

315 

328 

340 

352 

364  376 

358 

388 

400 

413 

425 

437 

449 

461 

473 

485  497 

1 

1.2 

359 

509 

522 

534 

.546 

558 

570 

582 

594 

606  618 

2 
3 

2.4 
3.6 

360 

630 

642 

654 

666 

678 

691 

703 

715 

727  739 

4 

4.8 
6.0 
7.2 

361 

751 

763 

775 

787 

799 

811 

323 

835 

847  859 

5 
6 

362 

871 

883 

895 

907 

919 

931 

943 

955 

967  979 

7 

8.4 

363 

991  *003  *015 

*027 

*038 

*050  *062 

•07 1  *086  *098 

8 
9 

9.6 
10.8 

364 

56   110 

122 

1:34 

146 

158 

170 

182 

194 

205  217 

365 

229 

241 

253 

265 

277 

289 

301 

312 

324  336 

366 

348 

360 

372 

384 

3% 

407 

419 

431 

443  455 

367 

467 

478 

490 

502 

514 

526 

538 

549 

561  573 

368 

585 

597 

608 

620 

632 

644 

656 

667 

679  691 

369 

703 

714 

726 

738 

750 

761 

773 

"- 

"  "  •  • 

11 

370 

820 

832 

844 

855 

867 

879 

891 

902 

914  926 

1 

1.1 

371 

937 

949 

961 

972 

984 

996  *008  *019  *031  *043 

.2 
3 
4 

•J.  2 
3.3 
4.4 

372 

57   054 

066 

078 

089 

101 

113 

124 

136 

148  159 

373 

171 

183 

194 

206 

217 

229 

211 

252 

264  276 

5 

5.5 

374 

287 

299 

310 

322 

334 

345 

357 

368 

380  392 

6 

7 

6.6 

7.7 

375 

403 

415 

426 

438 

449 

461 

473 

484 

496  507 

8 
9 

8.8 
9.9 

376 

519 

530 

542 

553 

565 

588 

600 

611  623 

377 

634 

646 

657 

669 

680 

692 

703 

715 

726  738 

378 

749 

761 

772 

7-1 

807 

818 

830 

841  852 

379 

864 

875 

887 

-■.- 

910 

9-21 

933 

944 

955  967 

380 

978 

990  *001  *013  *024 

*035  *047  *058  *070  *081 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P 

.  P. 

062 


Logarithms  of  Numbers. 


Num.  380  to  419.     Log.  579  to  623. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

380 

57   978 

990  *001  *013  *024 

*035  *047  *058  *070  *081 

381 

58   092 

104 

115 

127 

138 

149 

161 

172 

184 

195 

382 

206 

218 

229 

240 

252 

263 

274 

286 

297 

309 

383 

320 

331 

343 

354 

365 

377 

388 

399 

410 

422 

384 

433 

444 

456 

467 

478 

490 

501 

512 

524 

535 

1 1 

385 

546 

557 

569 

580 

591 

602 

614 

625 

636 

647 

386 

659 

670 

681 

692 

704 

715 

726 

737 

749 

760 

1 
2 

2.2 

387 

771 

782 

794 

805 

816 

827 

838 

850 

861 

872 

3 

3.3 

388 

883 

894 

906 

917 

928 

939 

950 

961 

973 

984 

4 
5 
6 

4.4 
5.5 

6.6 

389 

995  *006  *017  *028  *040 

*051  *062 

*073 

*084 

*095 

390 

59   106 

118 

129 

140 

151 

162 

173 

184 

195 

207 

7 
8 

7.7 
8.8 

391 

218 

229 

240 

251 

262 

273 

284 

295 

306 

318 

9 

9.9 

392 

329 

340 

351 

362 

373 

384 

395 

406 

417 

428 

393 

439 

450 

461 

472 

483 

494 

506 

517 

528 

539 

394 

550 

561 

572 

583 

594 

605 

616 

627 

638 

649 

395 

660 

671 

682 

693 

704 

715 

726 

737 

748 

759 

396 

770 

780 

791 

802 

813 

824 

835 

846 

857 

868 

10 

397 

879 

890 

901 

912 

923 

934 

945 

956 

966 

977 

398 

988 

999  *010  *021  *032 

*043  *054  *065 

*076  *086 

1 

1.0 

399 

60   097 

108 

119 

130 

141 

152 

163 

173 

184 

195 

i 

2.0 
3.0 

400 

206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

4 
5 
6 

4.0 

5.0 
6.0 

401 

314 

325 

336 

347 

358 

369 

379 

390 

401 

412 

402 

423 

433 

444 

455 

466 

477 

487 

498 

509 

520 

7 

7.0 

403 

531 

541 

552 

563 

574 

584 

595 

606 

617 

627 

8 
9 

8.0 
9.0 

404 

638 

649 

660 

670 

681 

692 

703 

713 

724 

735 

405 

746 

756 

767 

778 

788 

799 

810 

821 

831 

842 

406 

853 

863 

874 

885 

895 

906 

917 

927 

938 

949 

407 

959 

970 

981 

991 

*002 

*013  *023  *034  *045  *055 

408 

61   066 

077 

087 

098 

109 

119 

130 

140 

151 

162 

409 

172 

183 

194 

204 

215 

225 

236 

247 

257 

268 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

411 

384 

395 

405 

416 

426 

437 

448 

458 

469 

479 

412 

490 

500 

511 

521 

532 

542 

553 

563 

574 

584 

413 

595 

606 

616 

627 

637 

648 

658 

669 

679 

690 

414 

700 

711 

721 

731 

742 

752 

763 

773 

784 

794 

415 

805 

815 

826 

836 

847 

857 

868 

878 

888 

899 

416 

909 

920 

930 

941 

951 

962 

972 

982 

993  *003 

417 

62   014 

024 

034 

045 

055 

066 

076 

086 

097 

107 

418 

118 

128 

138 

149 

159 

170 

180 

190 

201 

211 

419 

221 

232 

242 

252 

263 

273 

284 

294 

304 

315 

420 

325 

335 

346 

356 

366 

377 

387 

397 

408 

418 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

Logarithms  of  Numbers. 


563 


Num.  420  to  459.     Log.  623  to  662. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

420 

62   325 

335 

346 

::77 

397 

408 

418 

421 

428 

489 

449 

459 

469 

480 

490 

500 

511 

521 

422 

531 

542 

552 

562 

572 

583 

593 

603 

613 

624 

12 

634 

644 

655 

665 

675 

6t5 

696 

706 

716 

726 

424 

737 

747 

7".: 

767 

77- 

788 

798 

808 

818 

829 

425 

839 

849 

859 

870 

880 

890 

900 

910 

921 

931 

426 

941 

951 

961 

972 

982 

992 

•002 

*012 

♦022 

*033 

427 

63   043 

053 

063 

0,3 

083 

094 

104 

114 

124 

134 

428 

M4 

153 

165 

175 

165 

195 

205 

215 

225 

236 

10 

429 

246 

256 

266 

276 

286 

296 

306 

317 

327 

337 

430 

347 

357 

367 

377 

3*7 

397 

407 

417 

4'28 

438 

1 
2 

1.0 
2.0 

431 

448 

458 

468 

478 

488 

4'.'- 

508 

518 

528 

538 

3 

3.0 

432 

548 

558 

568 

579 

589 

599 

609 

619 

629 

639 

4 
5 
6 

4.0 
5.0 
6.0 

433 

649 

659 

669 

679 

689 

699 

709 

719 

729 

739 

434 
435 

749 
849 

759 
859 

769 
869 

779 
879 

789 
889 

799 
899 

809 
909 

819 
919 

829 
929 

839 
939 

7 
8 
9 

7.0 
8.0 
9.0 

436 

949 

959 

969 

979 

988 

998  *008  *018  *028  *038 

437 

64   048 

058 

068 

078 

088 

098 

108 

US 

128 

137 

438 

147 

157 

167 

177 

187 

197 

207 

217 

227 

237 

439 

246 

256 

266 

276 

286 

2% 

306 

316 

326 

335 

440 

345 

355 

365 

375 

385 

395 

404 

414 

424 

434 

441 

444 

4-54 

464 

473 

483 

493 

503 

513 

523 

532 

442 

542 

552 

562 

572 

582 

591 

601 

611 

621 

631 

443 

640 

650 

660 

670 

680 

689 

699 

709 

719 

729 

444 

738 

748 

75S 

768 

777 

7^7 

797 

807 

816 

826 

445 

836 

846 

856 

865 

875 

885 

895 

904 

914 

924 

9 

446 

933 

943 

953 

963 

972 

982 

992 

*002 

*011  *021 

1 

0.9 

447 

65   031 

040 

050 

060 

070 

079 

089 

099 

108 

118 

2 
3 
4 

1.8 
2.7 
3.6 

448 

128 

137 

147 

157 

167 

176 

186 

196 

205 

215 

449 
450 

225 
321 

234 
331 

244 
341 

254 
350 

263 
360 

273 
369 

283 

379 

292 
389 

302 
398 

312 
408 

5 

6 
7 

4.5 
5.4 
6.3 

451 

418 

427 

437 

447 

456 

466 

475 

485 

495 

504 

8 
9 

7.2 
8.1 

452 

514 

523 

533 

543 

552 

562 

571 

581 

591 

600 

453 

610 

619 

629 

639 

648 

658 

667 

677 

686 

6% 

454 

706 

715 

725 

734 

744 

75:; 

763 

772 

782 

79-2 

455 

801 

Ml 

820 

830 

839 

849 

858 

868 

877 

887 

4.56 

8% 

906 

916 

925 

944 

954 

963 

973 

457 

*0Ul  *011  *020  *030 

*039  *049  *058  *068  *077 

458 

66   087 

0% 

106 

115 

124 

134 

143 

153 

162 

172 

459 

181 

191 

200 

210 

219 

229 

238 

217 

257 

266 

460 

>-> 

304 

314 

323 

332 

31'J 

351 

361 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

564 


Logarithms  of  Numbers. 


Num.  460  to  499.     Log.  662  to  698. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

460 

66   276 

285 

295 

304 

314 

323 

332 

342 

351  361 

461 

370 

380 

389 

398 

408 

417 

427 

436 

445  455 

462 

464 

474 

483 

492 

502 

511 

521 

530 

539  549 

463 

558 

567 

577 

586 

596 

605 

614 

624 

633  642 

464 

652 

661 

671 

680 

689 

699 

708 

717 

727  736 

465 

745 

755 

764 

773 

783 

792 

801 

811 

820  829 

466 

839 

848 

857 

867 

876 

885 

894 

904 

913  922 

467 

932 

941 

950 

960 

969 

978 

987 

997  *006  *015 

468 

67   025 

034 

043 

052 

062 

071 

080 

089 

099  108 

10 

469 

117 

127 

136 

145 

154 

164 

173 

182 

191  201 

470 

210 

219 

228 

237 

247 

256 

265 

274 

284  293 

1 

2 

1.0 

2.0 

471 

302 

311 

321 

330 

339 

348 

357 

367 

376  385 

3 

3.0 

472 

394 

403 

413 

422 

431 

440 

449 

459 

468  477 

4 

5 
6 

4.0 
5.0 
6.0 

473 

486 

495 

504 

514 

523 

532 

541 

550 

560  569 

474 
475 

578 
669 

587 
679 

596 
688 

605 
697 

614 
706 

624 

715 

633 
724 

642 
733 

651  660 
742  752 

7 
8 
9 

7.0 
8.0 
9.0 

476 

761 

770 

779 

788 

797 

806 

815 

825 

834  843 

477 

852 

861 

870 

879 

888 

897 

906 

916 

925  934 

478 

943 

952 

961 

970 

979 

988 

997  *006  *015  *024 

479 

68   034 

043 

052 

061 

070 

079 

088 

097 

106  115 

480 

124 

133 

142 

151 

160 

169 

178 

187 

196  205 

481 

215 

224 

233 

242 

251 

260 

269 

278 

287  296 

482 

305 

314 

323 

332 

341 

350 

359 

368 

377  386 

483 

395 

404 

413 

422 

431 

440 

449 

458 

467  476 

484 

485 

494 

502 

511 

520 

529 

538 

547 

556  565 

485 

574 

583 

592 

601 

610 

619 

628 

637 

646  655 

9 

486 

664 

673 

681 

690 

699 

708 

717 

726 

735  744 

1 

0.9 

487 

753 

762 

771 

780 

789 

797 

806 

815 

824  833 

2 
3 

4 

1.8 
2.7 
3.6 

488 

842 

851 

860 

869 

878 

886 

895 

904 

913  922 

489 
490 

931 
69   020 

940 
028 

949 
037 

958 
046 

966 
055 

975 
064 

984 
073 

993 

082 

*002  *011 
090  099 

5 
6 

7 

4.5 
5.4 
6.3 

491 

108 

117 

126 

135 

144 

152 

162 

170 

179  188 

8 
9 

7.2 

8.1 

492 

197 

205 

214 

223 

232 

241 

249 

258 

267  276 

493 

285 

294 

302 

311 

320 

329 

338 

346 

355  364 

494 

373 

381 

390 

399 

408 

417 

425 

434 

443  452 

495 

461 

469 

478 

487 

496 

504 

513 

522 

531  539 

496 

548 

557 

566 

574 

583 

592 

601 

609 

618  627 

497 

636 

644 

653 

662 

671 

679 

688 

697 

705  714 

498 

723 

732 

740 

749 

758 

767 

775 

784 

793  801 

499 

810 

819 

827 

836 

845 

854 

862 

871 

880  888 

500 

897 

906 

914 

923 

932 

940 

949 

958 

966  975 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

Logarithms  op  Numbers. 


565 


Num.  500  to  539.     Log.  698  to  732. 


N 

L    0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

500 

C9   897 

906 

914 

922 

932 

940 

949 

968 

966  975 

501 

984 

992 

*oul  *010  *018 

*027 

*044  *053  *062 

502 

70   070 

079 

088 

096 

105 

114 

}■>■> 

131 

140  148 

503 

157 

165 

171 

191 

200 

209 

217 

226  234 

504 

243 

252 

260 

269 

278 

286 

295 

303 

312  321 

505 

329 

338 

346 

355 

364 

372 

381 

389 

398  406 

606 

415 

424 

432 

441 

449 

458 

467 

475 

484  492 

507 

501 

509 

518 

526 

535 

544 

552 

561 

569  578 

508 

586 

595 

603 

612 

621 

629 

638 

646 

655  663 

9 

509 

672 

680 

689 

697 

706 

714 

723 

731 

740  74'J 

510 

757 

766 

77  4 

7S3 

791 

800 

808 

817 

825  834 

1 
2 

0.9 
1.8 

511 

>iJ 

851 

859 

868 

876 

885 

893 

902 

910  919 

3 

2.7 

512 

927 

9:15 

944 

952 

961 

969 

978 

986 

995  *003 

4 
5 
6 

3.6 
4.5 
5.4 

513 

71   012 

020 

029 

037 

046 

054 

063 

071 

079  088 

514 
515 

096 
181 

105 
189 

113 

198 

122 
206 

130 

214 

139 
223 

147 
231 

155 
240 

164  172 
248  257 

7 
8 
9 

6.3 

7.2 
8.1 

516 

265 

273 

282 

290 

299 

307 

315 

324 

332  341 

517 

349 

357 

366 

374 

383 

391 

399 

408 

416  425 

518 

1 

441 

450 

458 

466 

475 

483 

492 

500  508 

519 

517 

525 

533 

542 

550 

559 

567 

575 

584  592 

520 

600 

609 

617 

625 

634 

642 

650 

659 

667  675 

521 

684 

692 

700 

709 

717 

725 

734 

742 

750  759 

522 

767 

775 

784 

792 

800 

809 

817 

825 

834  842 

523 

858 

867 

875 

883 

892 

900 

908 

917  925 

524 

933 

941 

950 

958 

966 

975 

983 

991 

999  *008 

525 

72   016 

024 

032 

041 

049 

057 

066 

074 

082  090 

8 

526 

099 

107 

115 

123 

132 

140 

148 

156 

165  173 

1 

0.8 

527 

181 

189 

198 

206 

214 

222 

230 

239 

217  25-5 

2 
3 
4 

1.6 
2.4 
3.2 

528 

263 

•_'72 

280 

288 

296 

304 

313 

321 

329  337 

529 
530 

346 

428 

354 
436 

362 

411 

370 
452 

378 
460 

387 
469 

395 

477 

403 
485 

411  419 
493  501 

■'. 
6 
7 

4.0 
4.8 
5.6 

531 

509 

518 

526 

534 

542 

5.50 

558 

567 

575  583 

8 
9 

6.4 
7.2 

532 

591 

599 

607 

616 

624 

632 

640 

648 

656  665 

533 

673 

681 

689 

697 

705 

713 

730 

738  746 

534 

754 

762 

770 

779 

787 

795 

803 

811 

819  827 

635 

835 

843 

852 

860 

■ 

876 

884 

892 

900  908 

536 

916 

925 

933 

941 

919 

957 

965 

973 

981  989 

537 

997  *006  *014  *022 

•030 

*038  *046  *0M 

062  *070 

538 

73   078 

066 

094 

102 

111 

119 

127 

135 

143  151 

539 

159 

167 

175 

183 

191 

199 

207 

215 

223  231 

540 

239 

247 

2.55 

263 

_-> 

-"■» 

2% 

304  312 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P. 

P. 

5C6 


Logarithms  of  Numbers. 


Sum 

.  540  to 

579. 

Log 

.  732  to  763. 

N 

L   0 

1 

2 

3 

4 

5 

6   7   8   9 

P.  P. 

540 

73   239 

247 

255 

263 

272 

280 

288  296  304  312 

541 

320 

328 

336 

344 

352 

360 

368  376  384  392 

542 

400 

408 

416 

424 

432 

440 

448  456  464  472 

543 

480 

488 

496 

504 

512 

520 

528  536  544  552 

544 

560 

568 

576 

584 

592 

600 

608  616  624  632 

545 

640 

648 

656 

664 

672 

679 

687  695  703  711 

546 

719 

727 

735 

743 

751 

759 

767  775  783  791 

547 

799 

807 

815 

823 

830 

838 

846  854  862  870 

548 

878 

886 

894 

902 

910 

918 

926  933  941  949 

8 

549 

957 

965 

973 

981 

989 

997  *005  *013  *020  *028 

550 

74   036 

044 

052 

060 

068 

076 

084  092  099  107 

1 
2 

0.8 
1.6 

551 

115 

123 

131 

139 

147 

155 

162  170  178  186 

3 

2.4 

552 

194 

202 

210 

218 

225 

233 

241  249  257  265 

4 
5 
6 

3.2 
4.0 

4.8 

553 

273 

280 

288 

296 

304 

312 

320  327  335  343 

554 

351 

359 

367 

374 

382 

390 

398  406  414  421 

7 
8 

5.6 

6.4 

555 

429 

437 

445 

453 

461 

468 

476  484  492  500 

9 

7.2 

556 

507 

515 

523 

531 

539 

547 

554  562  570  578 

557 

586 

593 

601 

609 

617 

624 

632  640  648  656 

558 

663 

671 

679 

687 

695 

702 

710  718  726  733 

559 

741 

749 

757 

764 

772 

780 

785  796  803  811 

560 

819 

827 

834 

842 

850 

858 

865  873  881  889. 

561 

896 

904 

912 

920 

927 

935 

943  950  958  966 

562 

974 

981 

989 

997  *005 

*012 

*020  *028  *035  *043 

563 

75   051 

059 

066 

074 

082 

089 

097  105  113  120 

564 

128 

136 

143 

151 

159 

166 

174  182  189  197 

565 

205 

213 

220 

228 

236 

243 

251  259  266  274 

7 

566 

282 

289 

297 

305 

312 

320 

328  335  343  351 

1 

0.7 

567 

358 

366 

374 

381 

389 

397 

404  412  420  427 

2 
3 
4 

1.4 
2.1 

2.8 

568 

435 

442 

450 

458 

465 

473 

481  488  496  504 

569 

511 

519 

526 

534 

542 

549 

557  565  572  580 

5 

6 

7 

3.5 
4.2 
4.9 

570 

587 

595 

603 

610 

618 

626 

633  641  648  656 

571 

664 

671 

679 

686 

694 

702 

709  717  724  732 

8 
9 

5.6 
6.3 

572 

740 

747 

755 

762 

770 

778 

785  793  800  808 

573 

815 

823 

831 

838 

846 

853 

861  868  876  884 

574 

891 

899 

906 

914 

921 

929 

937  944  952  959 

575 

967 

974 

982 

989 

997 

*005  *012  *020  *027  *035 

576 

76   042 

050 

057 

065 

072 

080 

087  095  103  110 

577 

118 

125 

133 

140 

148 

155 

163  170  178  185 

578 

193 

200 

208 

215 

223 

230 

238  245  253  260 

579 

268 

275 

283 

290 

298 

305 

313  320  328  335 

580 

343 

350 

358 

365 

373 

380 

388  395  403  410 

N 

L   0 

1 

2 

3 

4 

5 

6   7   8   9 

P.  P. 

LOO  IR1  i  SMS    OF    NUMBERS. 


.v,: 


Num.  580  to  619.     Log.  763  to  792. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

5S0 

76   343 

350 

358 

365 

373 

380 

395 

411:; 

41D 

8 

581 

418 

425 

440 

448 

455 

470 

177 

485 

582 

492 

500 

507 

515 

522 

537 

545 

552 

1 

■j 

u.o 
1.5 

567 

574 

604 

612 

619 

626 

634 

3 

2.4 

Gil 

649 

664 

671 

678 

- 

701 

708 

1 

3.2 

1.0 

585 

716 

723 

"  ■ 

745 

753 

760 

768 

77"> 

782 

6 

4.8 
5.6 

6.4 

790 

797 

• 

812 

819 

-27 

-  ; 

842 

849 

856 

7 
8 

687 

871 

879 

886 

901 

• 

916 

923 

930 

9 

7.2 

- 

938 

945 

900 

1 

'.C. 

982 

989 

997 

*004 

77   012 

019 

0-20 

034 

041 

048 

056 

063 

070 

590 

085 

093 

100 

1U7 

115 

122 

129 

137 

14  4 

151 

591 

159 

166 

17:1 

181 

188 

195 

203 

210 

217 

225 

E  - 

232 

240 

'J  47 

254 

262 

269 

276 

283 

291 

298 

593 

305 

313 

320 

327 

3J5 

342 

349 

357 

364 

371 

594 

379 

386 

393 

401 

408 

415 

422 

430 

437 

444 

452 

459 

466 

171 

4-1 

188 

495 

503 

510 

517 

596 

525 

532 

546 

554 

561 

568 

583 

590 

597 

597 

605 

612 

619 

627 

634 

641 

648 

656 

663 

7 

598 

670 

677 

685 

692 

699 

706 

714 

721 

7_~ 

735 

599 

743 

750 

757 

7«;i 

772 

779 

7-', 

79:: 

801 

808 

1 
2 

0.7 
1  4 

600 

815 

822 

830 

837 

844 

851 

859 

866 

873 

B80 

3 
4 

5 

2.1 
2.8 
3.5 

601 

887 

895 

902 

909 

916 

924 

931 

938 

945 

952 

602 

960 

967 

974 

981 

988 

996  *003  *010  *017  *025 

6 

4.2 

603 

7-   032 

039 

046 

053 

061 

068 

075 

082 

089 

097 

7 
8 
9 

4.9 
5.6 
6.3 

604 

104 

111 

118 

125 

132 

140 

147 

1.54 

161 

168 

605 

176 

183 

190 

197 

204 

211 

219 

226 

233 

240 

606 

247 

254 

262 

269 

276 

283 

290 

297 

305 

312 

607 

319 

326 

333 

340 

•117 

355 

362 

369 

376 

3S3 

608 

390 

- 

405 

412 

419 

426 

433 

440 

447 

455 

609 

462 

469 

476 

490 

497 

504 

512 

519 

526 

610 

533 

540 

547 

554 

561 

569 

576 

583 

590 

597 

611 

604 

611 

618 

625 

640 

647 

6-54 

661 

668 

612 

675 

•>2 

689 

6% 

704 

711 

718 

725 

732 

739 

613 

J 

" 

760 

77  4 

7-1 

789 

796 

802 

810 

614 

-17 

324 

83] 

-  - 

• 

- 

866 

37 

880 

615 

888 

895 

902 

909 

916 

923 

930 

944 

951 

616 

958 

965 

972 

979 

986 

993  *000  *007 

*014  *021 

617 

79   029 

036 

013 

050 

057 

064 

071 

078 

085 

092 

099 

106 

113 

120 

127 

134 

141 

148 

155 

162 

ciy 

169 

176 

183 

190 

197 

204 

211 

218 

225 

232 

620 

239 

246 

253 

274 

281 

j- 

295 

302 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

i 

P.  P. 

568 


Logarithms  op  Numbers. 


Num.  620  to  659.     Log.  792  to  819. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

620 

79   239 

246 

253 

260 

267 

274 

281 

288 

295 

302 

621 

309 

316 

323 

330 

337 

344 

351 

358 

365 

372 

622 

379 

386 

393 

400 

407 

414 

421 

428 

435 

442 

623 

449 

456 

463 

470 

477 

484 

491 

498 

505 

511 

624 

518 

525 

532 

539 

546 

553 

560 

567 

574 

581 

625 

588 

595 

602 

609 

616 

623 

630 

637 

644 

650 

626 

657 

664 

671 

678 

685 

692 

699 

706 

713 

720 

627 

727 

734 

741 

748 

754 

761 

768 

775 

782 

789 

628 

796 

803 

810 

817 

824 

831 

837 

844 

851 

858 

629 

865 

872 

879 

886 

893 

900 

906 

913 

920 

927 

630 

934 

941 

948 

955 

962 

969 

975 

982 

989 

996 

631 

80   003 

010 

017 

024 

030 

037 

044 

051 

058 

065 

632 

072 

079 

085 

092 

099 

106 

113 

120 

127 

134 

633 

140 

147 

154 

161 

168 

175 

182 

188 

195 

202 

634 

209 

216 

223 

229 

236 

243 

250 

257 

264 

271 

635 

277 

284 

291 

298 

305 

312 

318 

325 

332 

339 

636 

346 

353 

359 

366 

373 

380 

387 

393 

400 

407 

7 

637 

414 

421 

428 

434 

441 

448 

455 

462 

468 

475 

638 

482 

489 

496 

502 

509 

516 

523 

530 

536 

543 

1 

0.7 

639 

550 

557 

564 

570 

577 

584 

591 

598 

604 

611 

2 
3 

1.4 

2.1 

640 

641 

618 
686 

625 
693 

632 
699 

638 
706 

645 
713 

652 
720 

659 
726 

665 
733 

672 

740 

679 

747 

4 
5 
6 

2.8 
3.5 
4.2 

642 

754 

760 

767 

774 

781 

787 

794 

801 

808 

814 

7 

4.9 

643 

821 

828 

835 

841 

848 

855 

862 

868 

875 

882 

8 

Q 

5.6 
6.3 

644 

889 

895 

902 

909 

916 

922 

929 

936 

943 

949 

%/ 

645 

956 

963 

969 

976 

983 

990 

996  *003  *010  *017  ' 

646 

81   023 

030 

037 

043 

050 

057 

064 

070 

077 

084 

647 

090 

097 

104 

111 

117 

124 

131 

137 

144 

151 

648 

158 

164 

171 

178 

184 

191 

198 

204 

211 

218 

649 

224 

231 

238 

245 

251 

258 

265 

271 

278 

285 

650 

291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

651 

358 

365 

371 

378 

385 

391 

398 

405 

411 

418 

652 

425 

431 

438 

445 

451 

458 

465 

471 

478 

485 

653 

491 

498 

505 

511 

518 

525 

531 

538 

544 

551 

654 

558 

564 

571 

578 

584 

591 

598 

604 

611 

617 

655 

624 

631 

637 

644 

651 

657 

664 

671 

677 

684 

656 

690 

697 

704 

710 

717 

723 

730 

737 

743 

750 

657 

757 

763 

770 

776 

783 

790 

796 

803 

809 

816 

658 

823 

829 

836 

842 

849 

856 

862 

869 

875 

882 

659 

889 

895 

902 

908 

915 

921 

928 

935 

941 

948 

660 

954 

961 

968 

974 

981 

987 

994  *000  *007  *014 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

Logarithms  of  Numbers. 


569 


Num. 

660  to 

699. 

Log. 

819 

to  845. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

660 

81   964 

961 

968 

971 

981 

994  *000  *007  *014 

7 

661 

82   020 

027 

040 

046 

0r>3 

060 

066 

073 

079 

1 

0.7 

1.1 

662 

066 

09*2 

099 

105 

112 

119 

125 

132 

138 

145 

f,„  . 

151 

158 

164 

171 

178 

184 

191 

197 

20 1 

210 

3 

2.1 

664 

217 

22:'. 

236 

243 

249 

256 

263 

269 

276 

4 
5 

3.5 

665 

282 

289 

295 

302 

- 

315 

321 

328 

334 

341 

6 
7 
8 

4.2 
4.9 
5.6 

666 

347 

354 

360 

3 

380 

387 

393 

400 

406 

667 

413 

419 

426 

432 

439 

415 

452 

458 

465 

471 

9 

6.3 

668 

478 

484 

491 

497 

504 

510 

517 

523 

530 

536 

669 

543 

549 

556 

562 

569 

575 

582 

5» 

595 

601 

670 

607 

614 

620 

627 

633 

640 

646 

653 

659 

666 

671 

672 

679 

692 

698 

705 

711 

718 

724 

730 

672 

737 

743 

750 

756 

763 

769 

776 

782 

789 

795 

673 

902 

808 

814 

821 

827 

834 

840 

847 

853 

860 

674 

866 

872 

879 

885 

892 

898 

905 

911 

918 

924 

675 

930 

937 

943 

9-50 

9.56 

963 

969 

975 

982 

y^ 

676 

995  *001  *008  *014  *020 

•027  *033  *040  *046  *052 

677 

83   059 

065 

072 

078 

0S5 

091 

097 

104 

110 

117 

6 

678 

123 

129 

136 

142 

149 

155 

161 

168 

174 

181 

679 

187 

193 

200 

206 

213 

219 

2-25 

232 

238 

245 

1 
2 

0.6 
1.2 

680 

251 

257 

264 

270 

276 

283 

289 

2% 

302 

308 

3 
4 

5 

1.8 
2.4 
3.0 

681 

315 

321 

327 

334 

340 

317 

353 

359 

366 

372 

6*2 

378 

::--. 

391 

398 

404 

410 

417 

423 

429 

436 

6 

3.6 

683 

442 

148 

155 

461 

467 

474 

480 

487 

493 

499 

7 
8 
9 

4.2 
4.8 
5.4 

684 

506 

512 

518 

525 

531 

537 

544 

5-50 

556 

563 

685 

569 

575 

582 

588 

594 

601 

607 

613 

620 

626 

6*6 

632 

639 

645 

651 

658 

664 

670 

677 

683 

689 

687 

696 

702 

708 

715 

721 

727 

734 

740 

746 

753 

r,~ 

759 

7iV> 

771 

778 

7-1 

790 

797 

803 

809 

816 

822 

828 

835 

841 

947 

853 

860 

966 

872 

879 

690 

885 

891 

897 

904 

910 

916 

923 

929 

935 

942 

691 

948 

954 

960 

967 

973 

979 

985 

992 

998  *004 

692 

94  on 

017 

023 

029 

036 

042 

048 

055 

061 

067 

693 

073 

080 

086 

092 

098 

105 

111 

117 

123 

130 

694 

136 

142 

148 

155 

161 

167 

173 

180 

186 

192 

695 

198 

205 

211 

217 

223 

230 

236 

212 

248 

255 

696 

261 

267 

273 

a 

286 

292 

298 

305 

311 

317 

697 

323 

330 

336 

342 

348 

354 

361 

367 

373 

379 

698 

386 

392 

398 

404 

410 

417 

423 

429 

435 

442 

699 

448 

454 

460 

466 

47.1, 

479 

485 

491 

497 

504 

700 

510 

516 

522 

528 

541 

547 

553 

559 

566 

N 

L   0 

1 

2 

3 

4 

i   5 

6 

7  . 

8 

9 

P.  P. 

570 


Logarithms  of  Numbers. 


Num. 

700  to  739. 

Log 

.  845  to  869. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

700 

84   510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

701 

572 

578 

584 

590 

597 

603 

609 

615 

621 

628 

702 

634 

640 

646 

652 

658 

665 

671 

677 

683 

689 

703 

696 

702 

708 

714 

720 

726 

733 

739 

745 

751 

704 

757 

763 

770 

776 

782 

788 

794 

800 

807 

813 

705 

819 

825 

831 

837 

844 

850 

856 

862 

868 

874 

706 

880 

887 

893 

899 

905 

911 

917 

924 

930 

936 

707 

942 

948 

954 

960 

967 

973 

979 

985 

991 

997 

708 

85   003 

009 

016 

022 

028 

034 

040 

046 

052 

058 

709 

065 

071 

077 

083 

089 

095 

101 

107 

114 

120 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

711 

187 

193 

199 

205 

211 

217 

224 

230 

236 

242 

712 

248 

254 

260 

266 

272 

278 

285 

291 

297 

303 

713 

309 

315 

321 

327 

333 

339 

345 

352 

358 

364 

714 

370 

376 

382 

388 

394 

400 

406 

412 

418 

425 

715 

431 

437 

443 

449 

455 

461 

467 

473 

479 

485 

716 

491 

497 

503 

509 

516 

522 

528 

534 

540 

546 

717 

552 

558 

564 

570 

576 

582 

588 

594 

600 

606 

6 

718 

612 

618 

625 

631 

637 

643 

649 

655 

661 

667 

719 

673 

679 

685 

691 

697 

703 

709 

715 

721 

727 

1 
2 

U.B 
1.2 

720 

721 

733 
794 

739 
800 

745 
806 

751 
812 

757 
818 

763 

824 

769 

830 

775 
836 

781 
842 

788 
848 

3 
4 
5 

1.8 
2.4 
3.0 

722 

854 

860 

866 

872 

878 

884 

890 

896 

902 

908 

§ 

3.6 

723 
724 

914 
974 

920 
980 

926 

986 

932 

992 

938 
998 

944  950  956  962  968 
*004  *010  *016  *022  *028 

7 
8 
9 

4.2 
4.8 
5.4 

725 

86   034 

040 

046 

052 

058 

064 

070 

076 

082 

088 

726 

094 

100 

106 

112 

118 

124 

130 

136 

141 

147 

727 

153 

159 

165 

171 

177 

183 

189 

195 

201 

207 

728 

213 

219 

225 

231 

237 

24:i 

249 

255 

261 

267 

729 

273 

279 

285 

291 

297 

303 

308 

314 

320 

326 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

731 

392 

398 

404 

410 

415 

421 

427 

433 

439 

445 

732 

451 

457 

463 

469 

475 

481 

487 

493 

499 

504 

733 

510 

516 

522 

528 

534 

540 

546 

552 

558 

564 

734 

570 

576 

581 

587 

593 

599 

605 

611 

617 

623 

735 

629 

635 

641 

646 

652 

658 

664 

670 

676 

682 

736 

688 

694 

700 

705 

711 

717 

723 

729 

735 

741 

737 

747 

753 

759 

764 

770 

776 

782 

788 

794 

800 

738 

806 

812 

817 

823 

829 

835 

841 

847 

853 

859 

739 

864 

870 

876 

882 

888 

894 

900 

906 

911 

917 

740 

-■   ■■ 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

N. 

— — ■ 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

Logarithms  of  Ntmrers. 


571 


Num 

.  740  to 

779. 

Log 

.  869  to 

892 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

740 

86   923 

929 

935 

941 

9-17 

953 

958 

964 

970 

976 

741 

982 

•.— 

994 

999  *005 

*011  *017  *023  *029  *035 

742 

87   040 

046 

052 

058 

064 

070 

075 

081 

(-7 

093 

743 

099 

105 

111 

116 

122 

128 

134 

140 

146 

151 

744 

157 

163 

169 

175 

181 

186 

192 

198 

204 

210 

745 

216 

•>ii 

227 

233 

239 

245 

251 

256 

262 

268 

746 

274 

280 

'J- 

291 

297 

303 

309 

315 

320 

326 

747 

332 

338 

344 

349 

355 

361 

367 

373 

379 

384 

748 

390 

396 

102 

408 

413 

419 

12.5 

431 

437 

442 

749 

448 

154 

460 

466 

471 

477 

483 

489 

495 

500 

750 

506 

512 

518 

- 

.529 

541 

547 

552 

558 

751 

564 

570 

576 

581 

587 

593 

599 

604 

610 

616 

752 

622 

628 

633 

639 

645 

651 

656 

662 

668 

674 

753 

679 

6S5 

691 

697 

703 

708 

714 

720 

726 

731 

7-54 

737 

743 

749 

754 

760 

766 

772 

777 

783 

789 

755 

795 

800 

806 

812 

818 

823 

829 

835 

841 

846 

756 

852 

858 

864 

869 

875 

881 

887 

892 

898 

904 

::.: 

910 

915 

921 

927 

933 

938 

944 

9.50 

955 

961 

6 

758 

967 

973 

978 

9^ 

990 

996  *001  *007  *013  *018 

i  /\  *• 

759 

88   024 

030 

036 

041 

047 

053 

058 

064 

070 

076 

1 
2 

u.o 
1.2 

760 

081 

087 

093 

098 

104 

110 

116 

121 

127 

133 

3 
4 

1.8 
2.4 

761 

138 

144 

1-50 

156 

161 

167 

173 

178 

184 

190 

5 

3.0 

762 

195 

201 

207 

213 

218 

224 

230 

235 

241 

247 

6 
7 
8 

3.6 
4.2 
4.8 

763 

252 

258 

270 

275 

281 

287 

292 

298 

304 

764 

309 

315 

321 

326 

332 

&38 

343 

349 

355 

360 

9 

5.4 

765 

366 

372 

377 

383 

389 

395 

400 

406 

412 

417 

766 

423 

429 

434 

440 

446 

451 

457 

463 

468 

474 

767 

180 

485 

491 

497 

502 

508 

513 

519 

525 

530 

768 

536 

.542 

.547 

553 

559 

564 

570 

576 

581 

587 

:•  < 

593 

598 

604 

610 

615 

621 

627 

632 

638 

643 

770 

649 

655 

660 

666 

672 

677 

683 

r-.i 

694 

700 

771 

705 

711 

717 

722 

728 

734 

739 

745 

750 

7.56 

772 

762 

767 

773 

779 

784 

790 

795 

801 

807 

812 

7- 

818 

324 

829 

835 

840 

846 

852 

857 

863 

868 

774 

874 

8S0 

885 

891 

897 

902 

908 

913 

919 

925 

77J 

930 

936 

941 

947 

953 

958 

964 

969 

975 

981 

77''. 

986 

992 

997 

•003  *009 

*014  *020  *025 

*031  *037 

777 

89   042 

048 

053 

059 

064 

070 

076 

081 

087 

09-2 

778 

098 

104 

109 

115 

120 

126 

131 

137 

143 

148 

779 

1.54 

159 

165 

170 

176 

182 

187 

193 

198 

204 

780 

209 

215 

221 

_  _ 

248 

254 

260 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

572 


Logarithms  of  Numbers. 


Num 

.  780  to 

819. 

Log 

.  892  to 

913. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

780 

89   209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

781 

265 

271 

276 

282 

287 

293 

298 

304 

310 

315 

782 

321 

326 

332 

337 

343 

348 

354 

360 

365 

371 

783 

376 

382 

387 

393 

398 

404 

409 

415 

421 

426 

784 

432 

437 

443 

448 

454 

459 

465 

470 

476 

481 

785 

487 

492 

498 

504 

509 

515 

520 

526 

531 

537 

786 

542 

548 

553 

559 

564 

570 

575 

581 

586 

592 

787 

597 

603 

609 

614 

620 

625 

631 

636 

642 

647 

788 

653 

658 

664 

669 

675 

680 

686 

691 

697 

702 

789 

708 

713 

719 

724 

730 

735 

741 

746 

752 

757 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 

791 

818 

823 

829 

834 

840 

845 

851 

856 

862 

867 

792 

873 

878 

883 

889 

894 

900 

905 

911 

916 

922 

793 

927 

933 

938 

944 

949 

955 

960 

966 

971 

977 

794 

982 

988 

993 

998  *004 

*009  *015  *020  *026  *031 

795 

90   037 

042 

048 

053 

059 

064 

069 

075 

080 

085 

796 

091 

097 

102 

108 

113 

119 

124 

129 

135 

140 

797 

146 

151 

157 

162 

168 

173 

179 

184 

189 

195 

5 

798 

200 

206 

211 

217 

222 

227 

233 

238 

244 

249 

799 

255 

260 

266 

271 

276 

282 

287 

293 

298 

304 

1 
2 

u.o 
1.0 

800 

309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

3 
4 

1.5 
2.0 

801 

363 

369 

374 

380 

385 

390 

396 

401 

407 

412 

5 

2.5 

802 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 

6 

3.0 
3.5 
4.0 

803 

472 

477 

482 

488 

493 

499 

504 

509 

515 

520 

7 
8 

804 

526 

531 

536 

542 

547 

553 

558 

563 

569 

574 

9 

4.5 

805 

580 

585 

590 

596 

601 

607 

612 

617 

623 

628 

806 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 

807 

687 

693 

698 

703 

709 

714 

720 

725 

730 

736 

808 

741 

747 

752 

757 

763 

768 

773 

779 

784 

789 

809 

795 

800 

806 

811 

816 

822 

827 

832 

838 

843 

810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 

811 

902 

907 

913 

918 

924 

929 

934 

940 

945 

950 

812 

956 

961 

966 

972 

977 

982 

988 

993 

998  *004 

813 

91   009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

814 

062 

068 

073 

078 

084 

089 

094 

100 

105 

110 

815 

116 

121 

126 

132 

137 

142 

148 

153 

158 

164 

816 

169 

174 

180 

185 

190 

196 

201 

206 

212 

217 

817 

222 

228 

233 

238 

243 

249 

254 

259 

265 

270 

818 

275 

281 

286 

291 

297 

302 

307 

312 

318 

323 

819 

328 

334 

339 

344 

350 

355 

360 

365 

371 

376 

820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

Logarithms  of  Ntmrers. 


.1 , ., 


Num.  820  to  859.     Log.  913  to  934. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9     P. 

P. 

820 

91   381 

387 

392 

397 

403 

408 

413 

418 

124 

129 

821 

434 

440 

415 

450 

155 

461 

466 

471 

177 

1--' 

822 

1-7 

192 

498 

503 

508 

514 

519 

524 

529 

5:::) 

823 

540 

.545 

551 

556 

561 

566 

572 

577 

- 

587 

824 

593 

g98 

603 

61 ... 

614 

619 

62 1 

630 

635 

640 

825 

645 

651 

6-56 

661 

666 

672 

677 

682 

687 

693 

826 

698 

703 

709 

711 

719 

721 

730 

735 

740 

715 

827 

751 

7.56 

761 

766 

772 

777 

782 

787 

793 

798 

828 

803 

808 

814 

819 

824 

829 

834 

840 

845 

850 

829 

855 

861 

866 

871 

876 

882 

887 

892 

897 

903 

830 

908 

913 

918 

924 

929 

934 

939 

944 

9.50 

955 

831 

960 

965 

971 

976 

981 

986 

991 

997 

*002 

*007 

832 

92   012 

018 

023 

028 

033 

038 

044 

049 

054 

059 

833 

065 

070 

075 

080 

085 

091 

096 

101 

106 

111 

834 

117 

122 

127 

132 

137 

143 

148 

153 

158 

163 

835 

169 

174 

179 

184 

189 

195 

200 

205 

210 

215 

836 

221 

226 

231 

236 

241 

247 

252 

2.57 

262 

267 

837 

273 

278 

283 

288 

293 

298 

304 

309 

314 

319 

5 

838 

324 

330 

335 

340 

345 

350 

355 

361 

366 

371 
423 

0.5 
1.0 

839 

376 

381 

387 

392 

397 

402 

407 

412 

418 

840 

128 

433 

138 

443 

449 

454 

459 

464 

469 

474    \ 

1.5 
2.0 

841 

480 

485 

490 

495 

500 

505 

511 

516 

521 

526    5 

2.5 

842 

531 

536 

542 

547 

552 

557 

562 

567 

572 

57-     6 

3.0 
3.5 
4.0 

843 

583 

588 

593 

598 

603 

609 

614 

619 

624 

629    g 

844 

634 

639 

645 

6-50 

6-55 

660 

665 

670 

675 

681    9 

4.5 

845 

686 

691 

696 

701 

706 

711 

716 

722 

727 

732 

846 

737 

742 

747 

752 

758 

763 

768 

773 

778 

783 

847 

788 

793 

799 

804 

809 

814 

819 

824 

829 

834 

848 

840 

845 

850 

855 

360 

365 

870 

875 

881 

886 

849 

891 

396 

901 

906 

911 

916 

921 

927 

932 

937 

850 

942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

851 

993 

998  *003  *008  *013 

*018  *021  *029  *034  *039 

852 

93   044 

049 

0-54 

059 

064 

069 

075 

0*0 

085 

090 

853 

095 

100 

105 

110 

115 

120 

125 

131 

136 

141 

854 

146 

151 

1-56 

161 

166 

171 

176 

181 

186 

192 

855 

197 

202 

207 

212 

217 

22-2 

227 

232 

2:".7 

242 

856 

247 

2  ".J 

258 

268 

273 

278 

283 

288 

293 

857 

298 

303 

308 

313 

323 

328 

334 

339 

344 

858 

349 

359 

364 

369 

374 

379 

384 

389 

394 

859 

399 

409 

414 

420 

425 

430 

435 

440 

445 

860 

450 

455 

460 

165 

470 

477. 

480 

185 

495 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9     P. 

P. 

574 


Logarithms  of  Numbers. 


Num.  860  to  899.     Log.  934  to  954. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

860 

93   450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

861 

500 

505 

510 

515 

520 

526 

531 

536 

541 

546 

862 

551 

556 

561 

566 

571 

576 

581 

586 

591 

596 

863 

601 

606 

611 

616 

621 

626 

631 

636 

641 

646 

864 

651 

656 

661 

666 

671 

676 

682 

687 

692 

697 

865 

702 

707 

712 

717 

722 

727 

732 

737 

742 

747 

866 

752 

757 

762 

767 

772 

777 

782 

787 

792 

797 

867 

802 

807 

812 

817 

822 

827 

832 

837 

842 

847 

868 

852 

857 

862 

867 

872 

877 

882 

887 

892 

897 

869 

902 

907 

912 

917 

922 

927 

932 

937 

942 

947 

870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

871 

94   002 

007 

012 

017 

022 

027 

032 

037 

042 

047 

872 

052 

057 

062 

067 

072 

077 

082 

086 

091 

096 

873 

101 

106 

111 

116 

121 

126 

131 

136 

141 

146 

874 

151 

156 

161 

166 

171 

176 

181 

186 

191 

196 

875 

201 

206 

211 

216 

221 

226 

231 

236 

240 

245 

876 

250 

255 

260 

265 

270 

275 

280 

285 

290 

295 

877 

300 

305 

310 

315 

320 

325 

330 

335 

340 

345 

5 

878 

349 

354 

359 

364 

369 

374 

379 

384 

389 

394 

1 

2 

0.5 
1.0 

879 

399 

404 

409 

414 

419 

424 

429 

433 

438 

443 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

3 
4 

1.5 
2.0 

881 

498 

503 

507 

512 

517 

522 

527 

532 

537 

542 

5 

2.5 

882 

547 

552 

557 

562 

567 

571 

576 

581 

586 

591 

6 

7 
8 

3.0 
3.5 

4.0 

883 

596 

601 

606 

611 

616 

621 

626 

630 

635 

640 

884 

645 

650 

655 

660 

665 

670 

675 

680 

685 

689 

9 

4.5 

885 

694 

699 

704 

709 

714 

719 

724 

729 

734 

738 

886 

743 

748 

753 

758 

763 

768 

773 

778 

783 

787 

887 

792 

797 

802 

807 

812 

817 

822 

827 

832 

836 

888 

841 

846 

851 

856 

861 

866 

871 

876 

880 

885 

889 

890 

895 

900 

905 

910 

915 

919 

924 

929 

934 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

891 

988 

993 

998  *002 

*007 

*012 

*017 

*022 

*027 

*032 

892 

95   036 

041 

046 

051 

056 

061 

066 

071 

075 

080 

893 

085 

090 

095 

100 

105 

109 

114 

119 

124 

129 

894 

134 

139 

143 

148 

153 

158 

163 

168 

173 

177 

895 

182 

187 

192 

197 

202 

207 

211 

216 

221 

226 

896 

231 

236 

240 

245 

250 

255 

260 

265 

270 

274 

897 

279 

284 

289 

294 

299 

303 

308 

313 

318 

323 

898 

328 

332 

337 

342 

347 

352 

357 

361 

366 

371 

899 

nt-fn 

OIO 

381 

386 

390 

395 

400 

405 

410 

415 

419 

900 

42A 

429 

434 

439 

444 

448 

453 

458 

463 

468 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

Logarithms  of   Nimbers. 


:,7:, 


Num.  900  to  939.     Log.  954  to  973. 


N 

L    0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

900 

95   421 

429 

134 

139 

111 

148 

453 

458 

463 

468 

901 

472 

477 

1-J 

487 

492 

497 

501 

506 

511 

5  If, 

902 

521 

'525 

530 

535 

540 

545 

550 

551 

559 

564 

903 

569 

571 

- 

583 

588 

593 

598 

602 

607 

612 

904 

617 

622 

626 

6  :i 

636 

611 

616 

650 

(155 

660 

905 

665 

670 

674 

679 

689 

694 

698 

703 

708 

906 

713 

718 

722 

727 

7:VJ 

737 

742 

716 

751 

756 

907 

761 

766 

770 

77.". 

780 

789 

794 

799 

804 

908 

809 

si:; 

818 

823 

828 

832 

837 

8-12 

847 

852 

900 

856 

861 

866 

871 

875 

SM) 

885 

890 

895 

899 

9J0 

904 

909 

914 

918 

923 

928 

933 

938 

942 

947 

911 

952 

957 

961 

966 

971 

976 

980 

985 

990 

995 

912 

999  *004  *009  *014  *019 

*023  *028  *033  *038  *042 

913 

96   047 

052 

057 

061 

066 

071 

076 

080 

085 

090 

914 

095 

099 

104 

109 

111 

118 

123 

128 

133 

137 

915 

142 

147 

152 

156 

161 

166 

171 

175 

180 

185 

916 

190 

194 

199 

204 

209 

213 

218 

223 

227 

232 

917 

237 

242 

21'', 

251 

256 

261 

265 

270 

275 

280 

5 

918 

284 

289 

294 

298 

303 

308 

313 

317 

322 

327 

1   n  e 

919 

332 

336 

34] 

346 

350 

355 

360 

365 

369 

374 

1 

2 

1.0 

920 

379 

384 

:,-s 

393 

398 

402 

407 

412 

417 

421 

3 
4 

1.5 
2.0 

021 

426 

431 

135 

440 

1  15 

450 

151 

459 

164 

168 

5 

2.5 

473 

478 

483 

487 

\\>: 

497 

501 

506 

511 

515 

6 
7 
8 

3.0 
3.5 
4.0 

923 

520 

525 

530 

.-..,1 

539 

544 

548 

553 

55S 

924 

567 

572 

577 

581 

586 

591 

595 

600 

605 

609 

9 

4.5 

925 

614 

619 

62 1 

628 

633 

638 

642 

647 

652 

656 

926 

661 

666 

670 

675 

680 

685 

689 

694 

699 

703 

927 

708 

713 

717 

722 

727 

731 

741 

715 

750 

9'28 

755 

759 

764 

769 

771 

778 

783 

788 

792 

797 

929 

802 

806 

811 

816 

820 

825 

830 

834 

Ml 

930 

848 

- 

858 

862 

867 

872 

876 

881 

•• 

890 

931 

895 

900 

904 

909 

914 

918 

923 

928 

937 

942 

916 

951 

956 

960 

965 

970 

974 

979 

984 

933 

988 

993 

'.''.•7 

*002  *007 

*011  *016  *021  *025 

'.'7 

039 

044 

049 

053 

058 

063 

067 

072 

077 

935 

081 

086 

090 

095 

100 

101 

109 

114 

118 

123 

128 

132 

137 

142 

146 

151 

1  -.5 

160 

165 

169 

937 

174 

179 

183 

188 

192 

197 

202 

•_'i  i»; 

211 

216 

938 

220 

225 

234 

239 

243 

248 

■J5:: 

257 

262 

939 

267 

271 

•J7<; 

280 

285 

290 

294 

299 

304 

- 

940 

313 

::17 

322 

327 

::::i 

340 

345 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

s 

9 

P. 

P. 

570 


Logarithms  of  Numbers. 


Num.  940  to  979.     Log.  973  to  991. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

940 

97   313 

317 

322 

327 

331 

336 

340 

345 

350 

354 

on 

359 

364 

368 

373 

377 

382 

387 

391 

396 

400 

912 

405 

410 

414 

419 

424 

428 

433 

437 

442 

447 

913 

451 

456 

460 

465 

470 

474 

479 

483 

488 

493 

941 

497 

502 

506 

511 

516 

520 

525 

529 

534 

539 

945 

543 

548 

552 

557 

562 

566 

571 

575 

580 

585 

946 

589 

594 

598 

603 

607 

612 

617 

621 

626 

630 

947 

635 

640 

644 

649 

653 

658 

663 

667 

672 

676 

948 

681 

685 

690 

695 

699 

704 

708 

713 

717 

722 

949 

727 

731 

736 

740 

745 

749 

754 

759 

763 

768 

5 

950 

772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

1 

0.5 

951 

818 

823 

827 

832 

836 

841 

845 

850 

855 

859 

2 

1.0 

1.5 

2.0 

952 

864 

868 

873 

877 

882 

886 

891 

896 

900 

905 

3 
4 

953 

909 

914 

918 

923 

928 

932 

937 

941 

946 

950 

5 

2.5 

954 

955 

959 

964 

968 

973 

978 

982 

987 

991 

996 

6 

7 

3.0 
3.5 

955 

98   000 

005 

009 

014 

019 

023 

028 

032 

037 

041 

8 
9 

4.0 
4.5 

956 

046 

050 

055" 

059 

064 

068 

073 

078 

082 

087 

957 

091 

096 

100 

105 

109 

114 

118 

123 

127 

132 

958 

137 

141 

146 

150 

155 

159 

164 

168 

173 

177 

959 

182 

186 

191 

195 

200 

204 

209 

214 

218 

223 

960 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

961 

272 

277 

281 

286 

290 

295 

299 

304 

308 

313 

962 

318 

322 

327 

331 

336 

340 

345 

349 

354 

358 

963 

363 

367 

372 

376 

381 

385 

390 

394 

399 

403 

964 

408 

412 

417 

421 

426 

430 

435 

439 

444 

448 

965 

453 

457 

462 

466 

471 

475 

480 

484 

489 

493 

4 

966 

498 

502 

507 

511 

516 

520 

525 

529 

534 

538 

1 

0.4 

967 

543 

547 

"552 

556 

561 

565 

570 

574 

579 

583 

2 

0.8 

968 

588 

592 

597 

601 

605 

610 

614 

619 

623 

628 

3 
4 

1.2 
1.6 

2.0 

969 

632 

637 

641 

646 

650 

655 

659 

664 

668 

673 

5 

970 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

6 

7 

2.4 
2.8 

971 

722 

726 

731 

735 

740 

744 

749 

753 

758 

762 

8 

3.2 

972 

767 

771 

776 

780 

784 

789 

793 

798 

802 

807 

9 

3.6 

973 

811 

816 

820 

825 

829 

834 

838 

843 

847 

851 

974 

856 

860 

865 

869 

874 

878 

883 

887 

892 

896 

975 

900 

905 

909 

914 

918 

923 

927 

932 

936 

941 

976 

945 

949 

954 

958 

963 

967 

972 

976 

981 

985 

977 

989 

994 

998  *003  *007 

*012 

*016  *021  *025  *029 

978 

99   034 

038 

043 

047 

052 

056 

061 

065 

069 

074 

979 

078 

083 

087 

092 

096 

100 

105 

109 

114 

118 

980 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

I 


Logarithms  of  Numbers. 


5~  -» 


Num.  980  to   1000.     Log.  991   to  999. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

980 

99   123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

981 

167 

171 

176 

180 

185 

189 

193 

198 

202 

207 

982 

211 

216 

220 

22| 

229 

233 

238 

242 

247 

251 

983 

255 

260 

264 

269 

273 

277 

282 

286 

291 

295 

984 

300 

304 

308 

313 

317 

322 

326 

330 

335 

339 

985 

344 

348 

352 

357 

361 

366 

370 

374 

379 

383 

986 

388 

392 

396 

401 

405 

410 

414 

419 

423 

427 

987 

432 

436 

441 

445 

449 

454 

458 

463 

467 

471 

988 

470 

480 

484 

489 

493 

498 

502 

506 

511 

515 

989 

520 

524 

528 

533 

537 

542 

546 

550 

555 

559 

4 

990 

991 

504 
607 

568 
612 

572 
616 

577 
621 

5S1 
625 

585 
629 

590 
634 

594 
638 

599 
642 

603 
647 

1 
2 
3 

0.4 
0.8 
1  2 

992 

651 

656 

660 

664 

669 

673 

677 

682 

686 

691 

4 

1.6 

993 

695 

699 

704 

708 

712 

717 

721 

726 

730 

734 

5 

2.0 

994 

739 

743 

747 

752 

756 

760 

765 

769 

774 

778 

6 

7 

2.4 
2.8 

995 

7S2 

787 

791 

795 

800 

804 

808 

813 

817 

822 

8 
9 

3.2 
3  6 

996 

826 

830 

835 

839 

843 

848 

852 

856 

861 

865 

997 

870 

874 

878 

883 

887 

891 

896 

900 

904 

909 

998 

913 

917 

922 

926 

930 

935 

939 

944 

948 

952 

999 

957 

961 

965 

970 

974 

978 

983 

987 

991 

996 

1000 

000   000 

043 

087 

130 

174 

217 

200 

304 

347 

391 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

Logarithms  of  Important  Numbers. 


J 

dumber. 

Logarithm. 

7T 

— 

3.141  593 

0.497  150 

l» 

= 

4.188  790 

0.622  089 

1* 

= 

0.523  599 

1.718  999 

1 

n 

= 

0.318  310 

1.502  850 

7T°- 

= 

9.869  604 

0.994  300 

1 

= 

0.101  321 

1.005  700 

1  M 

= 

1.772  454 

0.248  575 

1 

1  TT 

= 

0.564  190 

T.751  425 

fw 

= 

1.464  592 

0.165  717 

1 

= 

0.682  784 

1.834  283 

= 

1.240  701 

0.093  667 

INDEX. 


a.  8,  45,  47.  18,  54 
Acacia.  47 3 
Acres  into  hectares,  ."01 
Admiral  anchors,  322,  323 
Admiralty  cables.  416,  417 
"       '   ('(instant,  187 
"         knot,  488 
"         turnbuckles,  .'575 
Agriculture,   dept.  of   regulations, 

111 
Air.  47:; 
Alder,  473 

Algebraical  signs,  ix 
Alleyways,  cattle.  112 
Allowances  for  Bplices,  381 
Alteration  in  trim  through  shipping 

a  weight,  "JO 
Aluminium,  cast,  473 
sheet,  473 
"  bronze, 473 

Analysis  .lata.  Kirk's,  ;i4.  95 
Anchors.  Admiral.  322,  3'_*3 
"        Baldt,  318,  319 
"        Hall,  320,  321 
44        Ingletield,  324 
Angle  steel,  weight  of,  120-124 
Angle-bulb,  weight  of,  155-160 
Animals,  space  allotted  to,  112 
Antimony,  47:; 
Anthracite.  473 
Apple  wood,  473 

Approximate  rule  for  C.  of  B.,  12.  45 
"  rule  for  L.  B.  31.,  17 

"  rule  for  M",  19 

Area  of  circles,  513-520 

"  of  L.  W*.  L.  and  co- 

efficient a,  8, 45,  47, 
48,54 
Area  of  midship  section  and  coeffi- 
cient 0,  10 
"     of  propeller  brackets,  109,  110, 

286 
"     of  water  plane,  . 
Asbestos  board,  17:; 
Ash,  47:; 
Asphalte,  47:; 

Awning  decked  vessel,  77,  82,  86 
A  \.-s,  tire,  448 

/3,  10,  45,  47,  48,  57 
Bal»l»it  metal.  47:; 
Balanced  rudders,  106,  281 


079 


Baldt  anchors.  318,  319 

Bar  keel.  275,276 

liar  lev.  47:: 

Barrels,  448 

Basalt,  47:5 

Battening  bar,  305 

Beams,  295-300 

Beam  bending  moments,  212,  213 

"     camber,  51,  76,  295 

44      collars,  300 

"      knees,  296,  297,  299 
Beckets,  395 
Beech,  47:; 

B.lay  pins,  size  of,  331 
Bells,  proportions  of  ship's,  330 

44      size  and  weight  of,  331 
Bell  metal,  47:: 
Bending  moments  of  pins,  24(3.  247 

"  "  "   stress.  204 

Bilge  diagonal  coefficient,  45,  47,  48, 

55,57 
Bill  of  material,  315 
Birch,  473 
Bismuth,  473 
Bitts,  towing,  368 
Bituminous  coal,  473 
Bitumastic  cement,  294 

"  "        solution,  473 

Block  coefficient  S,  7,  45,  47,  48 
Blocks,  393-398 

44        cat  and  fish,  394 

"        clump,  394 

"        cheek,  394 

"        fiddle,  393 

44        gin,  394 

"         snatch,  393 

44        wrecking,  394 

"        sheaves  for,  394 

"        shackles  for,  394 

44        standard  iron,  334,  335 

"         weight  of,  396,  397 
Board  of  Trade  regulations,  428-439 
Boats,  420-427 

davits,  341 

44       proportions  of,  421 

"       scantlings  of.  428 

44      rules  and  regulations,  428-448 

44       weight  of,  396,  397 
Bodv  plan  of  Oceanic,  57 
Body  poet,  278 
Bollards,  proportion-  of,  332 

size  and  weight  of,  333 


580 


Index 


Bolts  and  nuts,  U.  S.  Standard,  336, 
337 
"     and    nuts,   Whitworth    Stan- 
dard, 480 
11     and  nuts,  weight  of,  481 
B.  M.,  13 
Bossing  around  shafts,  58,  59,   110, 

287,  288 
Boss  barrel,  59,  110,  286 
Bossing,  fairing  the,  58,  59,  110 
Bottom  half-breadth,  5 
Boxes,  stuffing,  371 
Boxwood,  473 
Braces,  279,  285 
Brackets,  area  of  propeller,  109,  110, 

286 
Bracket  knees,  296,  297,  299 
Brass,  473 

"       sidelights,  weight  of,  369 
"       Avire,  473 
Breaking  strength  of  chains,  234, 235 
Brick,  473 
Brickwork,  473 
Bridge  house,  77,  300 
Bridle  beams,  305 
British  corporation  rudder  formula, 

108 
British  Board  of  Trade  regulations, 

428-439 
Bronze,  473 
Buckets,  fire,  448 
Builders'  old  measurement  tonnage, 

472 
Built  columns,  301 
Bulb  angle,  weight  of,  155-160 
"      plate,  weight  of,  161,  162 
"      tee,  weight  of,  163-170 
Bulkheads,  307,  308 
Bulkhead  collars,  289,  307 
"  collision,  307 

"  liners,  308 

"  plating,  308 

"  stiffeners,  308 

Bullivant's  thimbles,  372 
Burton,  Spanish,  400,  401 
Butts,  plating,  310-314 

shift  of,  310 
Buttstraps,   Lloyd's    table  of,    260, 
261 
"  strength  of  riveted,  267 

"  U.S.  Navy,  table  of,  258 

Calculations,  ship,  1-201 

Calculation  of  G.  Z.,  40,  41 

Calories  into  thermal  units,  507 

Camber  of  ways,  102 

Camphor,  474 

Capacities  of  circular  tanks,  484 
"         of  lifeboats,  421,  430 
"         of  rectangular  tanks,  482, 
483 


Carlings,  300 

Cast  steel  rudder,  280 

"    steel,  weight  of,  477 
Cat  and  fish  blocks,  394 
Cattle  alleyways,  112 

"      fittings,  weight  of,  112 
"      transport  of,  111 
Catting  hooks,  340 
Caulking,  308 
Cedar,  474 

Ceiling  on  tanks,  294 
Cement,  bitumastic,  294 

"         Louisville,  474 

"         Portland,  474 

"         Roman,  474 
Centimetres  to  inches,  490 
Centre  keelson,  276,  277 
Centre  of  buoyancy,  11,  17,  26,  27, 45, 

"      of    buoyancy      by     Tchiby- 
scheff's  rule,  26,  27 

"      of  buoyancy  longitudinally, 
12, 18,  25 

"      of  flotation,  16,  18,  29 

"       of  gravity,  175-177 

"      of  gravity  coefficient  "  g,"  45; 
48 

"      vertical  girder,  276,  277,  292 
Chafing  pieces,  308 
Chain  slips,  proportions  of,  370 
Chain,  rigging,  398 
Chalk,  474 
Change  of  trim,  18 
Channel  bars,  weight  of,  135-144 

floors,  291 
Characteristic  of  logarithm,  553 
Charcoal,  474 
Cheek  blocks,  394 
Cherry,  474 
Chestnut,  474 

Cheval-vapeur  into  horse-power,  506 
Circles,  circumference  and  area  of, 

513-520 
Circle,  formulae  for,  513 
Circumference  and  area  of  circles, 

513-520 
Clay,  474 
Cleats,  belay,  338 
"        hatch,  304 
Clips,  wire  rope,  387 
Clump  blocks,  394 
Coal,  474 

Coefficient  a,  8,  45,  47,  48,  54 
"  8,  10,  45,  47,  48,  57 

"  S  (fineness), 7, 45, 47, 48,  7g 

g  (gravity),  48 
"  i  (inertia),  49 

Coir  rope,  392 
Collars,  beam,  300 

"         bulkhead,  289,  307 
Collision  bulkhead,  307 
I    Columns,  built,  301 


Index 


581 


Columns,  strength  of,  217-286 

Compressive  stress,  204 

Constants,  admiralty,  186,  187 

Corner  angles,  hatch,  3<H 

Correction     for     variations     (free- 
board), 83 

Cotton  rope,  392 

Coupling  bolts,  27'.),  28." 

palm  (rudder),  279,  280,  285 

Corera,  batch,  305 

Cowl  ventilators,  377 

Cowls,  weight  of,  376 

Crane  hooks,  339 

Cranes,  dimensions  of  anchor,  328 
stresses  on,  325-327 

Cross  curves  of  stability,  42 

Cubic  centimetres  into  cubic  inches, 

498 

M      decimetres  into  cubic  feet,  502 

"      feet  into  cubic  decimetres,  502 

"      inches  into  cubic  centimetres, 

498 
"      metres  into  cubic  yards,  499 
"     yards  into  cubic  metres,  499 

Cut  frames,  289 

Cypress,  474 

S,  coefficient,  7,  45,  47,  48,  72 
Data,  Kirk's  analysis,  94,  95 
launching,  102,  103 
"        steamers,  200,  201 
Davits,  diameters  of,  341 
Deals,  Riga,  474 
Deck  girders,  300 
Declivity  of  ways,  102 
Deductions  for  erections  (freeboard), 

74,83 
Deep  framing,  290 

Department  of  agriculture  regula- 
tions, 111 
Derrick  rigging,  406,  407 
Design,  44-63 

Designing  the  bossing,  58,  59 
Details  of  fittings,  313-377 
"        standardizing,  313 
"        of  structure,  274-313 
"       the  preparation  of,  315 
Diagram  of  bilge  diagonals,  55 

of  L.W.L.  half-breadths,  56 
Dimensions  for  freeboard.  74 
"  for  tonnage,  461 

Displacement,  1,  6,  24,  45 
"  sections.  4 

"  sheet     by     Tchibys- 

cheff 's  rule,  24 
"  table.  6,  24 

Division  boards,  cattle,  112 
Donkey  boiler,  449 
Doubling  plates,  303,  312 
Doublings  at  breaks,  312,  313 
»«         at  hatchways,  303 


e,  Relation  coefficient,  47,  48 
Earth,  474 

Ebonv,  474 

Effect  "f  form  of  waterline,  .'54-37 

Effective  horse-power,  194,  195 

Elasticity,  204 

Elements  of  angles,  237,  238 
of  bulb-angles,  239 
"         of  circular  sections,  216 
"         coefficients     for     various 

types,  44,  47,  48 
"         of  deck  beams.  240,  241 
'*  of  marine  engines,  60,  61 

of  sections,  208,  209 
"  of  tee  bars,  242,  243 
"         of  zee  bars,  244,  245 

Elm,  474 

Emergency  chains,  280 

Emerv,  474 

End  floors,  291 

Engines,  elements  of  marine,  60,  61 

Engine  room  lengths,  63 

Equipment,  40S-472 

Lloyd's,  408,  410,  411 
"  numeral,  408,  409 

"  weights,  413,  414 

Evebolts.  standard,  346 

Eves,  pad,  356,  357 
"      worked,  367 

Explanation  of  tables  of  metacen- 
tres,  31-33 

Exponent  of  logarithm,  553 

Factors  Of  safety,  206,  207 
Fairing  the  bossing,  58,  59 

"       the  oxter,  62 

"       plate  lines,  308,  309,  311 
Fairleads,  proportions  of,  347 

"  weight  of,  347 

Falls,  cargo  and  purchase,  383,  406, 

407 
Feet  to  metres,  496 
Fiddle  blocks,  393 
Figureheads  and  lacing  pieces,  52 
Fir, 474 

Fitting  of  pillars,  303 
Fittings,  details  of,  313-377 

weight  of  cattle,  112 

"        weight  of  horse,  113 
Flagging,  477 
Flanges,  lead  pipe,  348 

"         standard  pipe,  349 

"         ventilation,  350 
Flanged  floors,  290,  291 
Flat  plate  keels.  276,  277 
Flexible  steel  wire  ropes,  382,  383 
Flint.  474 

Floor  brackets,  291,  292 
Floors,  290,  291 

at  ends.  291 

"       channel,  291 


582 


Ind 


ex 


Floors,  flanged,  290,  291 
"       in  inner  bottom,  292 
"       ordinary,  291 
"       watertight,  291 

Flush  deck  vessel,  77 

Footboards,  cattle,  112 

Footlocks,  cattle,  112 

Footpounds     into    kilograminetres, 
506 

Foot-tons  into  tonnes-metres,  507 

Formulae  for  the  circle,  513 

Frame  doublings,  287,  288,  289 

Framing,  288-290 

Frame  riveting,  271 

Framing  of  superstructure,  289,  290 

Franklin  Institute  standard  bolts, 
337 

Freeboard,  73-92 

"  examples  of,  84-87 

"  tables,  notes  on,  83 

"  tables,  79-82 

"         '  marks,  89 

Freeboards  for  awning  deckers,  82-86 
"  for  freighters,  79,  80,  84 

"  for  shelter  deckers,  87, 88 

"  for  spar  deckers,  81,  85 

Freeing  port  area,  76 

Freestone,  474 

French  measures,  495-507 

Functions,  natural  trigonometrical, 
508-512 

Furnaced  plates,  311 

Garboard  strake,  275,  276 
Germanischer,  Lloyd's  rudder  form- 
ula, 108 
Gin  blocks,  394 

Glands,  stuffing  boxes  and,  371 
Glass,  475 
Gold,  475 
Granite,  475 
Graphite,  475 
Grains  into  grammes,  505 
Grammes  into  grains,  505 
Grammes  into  ounces,  505 
Greenheart,  475 
Gudgeons,  278,  279,  285 
Gum,  475 
Gunmetal,  475 
Gun  tackle  purchase,  400 
Guys,  406,  407 
Guy  purchase,  406,  407 
Gypsum,  475 

Hall  anchors,  320,  321 
Hand  wheels,  standard,  351,  352 
Hatches,  303 
Hatch  cleats,  304 

"      corner  doublings,  304 

"      covers,  305 

"      fore  and  afters,  305 


Hatch  lashing  rings,  305 

"      edges,  305 

"      wedges,  305 
Hatching,  standard  sectional,  316 
Hawse  pipes,  proportions  of,  354 

"      pipes,  Aveight  of,  355 
Hawthorn,  475 
Hay,  475 
Hazel,  475 

Headboards,  cattle,  112 
Hectares  into  acres,  501 
Heel  bearing  of  rudders,  280 
Heels,  stanchion,  303 
Hemlock,  475 
Hemp  cordage,  391 

"      rules  for  strength  of,  391 
Hold  pillars,  301-303 
Holes  through  shell,  312,  313 
Hood  end  plates,  278,  313 
Hooks  for  blocks,  395 

"      catting,  340 

"      crane, 339 

"      match,  387,  395 

"      sister,  387,  395 
Hornbeam,  475 
Horse  fittings,  weight  of,  113 
Horse-power  into  cheval-vapeur,  506 
Horse  stalls,  112 
Houseline,  392 

I  section,  weight  of,  145-150 
Ice,  475 

Immersion,    passing    from    salt  to 
fresh  water,  9 
"  tons  per  inch,  8 

Inch,  graphic  division  of  the,  317 
Inches  to  centimetres,  496 
India-rubber,  475 
Indicated  horse-power,  195,  201 
Inertia  coefficient,  17,  44 

"      moment  of,  205,  208,  209,  211, 

212,  215,  216,  217 
"      moment  of  for  circular  sec- 
tions, 216,  217 
Inglefield  anchors,  324 
Inner  bottoms,  292-295 
Inspection     laws,     American    and 

British,  111,  428-439,  440-460 
Interlocking  rubber  tiling,  477 
Intercostal  plates,  306 
Iron,  cast,  475 

"    wrought,  475 
Ironwood,  475 
Ivory, 475 

JTackwood,  475 

Jogging,  311 

Johnson's  formula  for  columns,  218 
"         formula  for   steel  hulls, 
116 


Index 


583 


Keel»,  275,  276 

Keel  doublings,  2.7 

"     scarphs,  275 
Keelsons,  306,  307 
Keys  and  keyways,  353 
Kevs,  ping  cock,  358 
Kilogrammes  into  pounds,  504 

ii  per  sq.  cm.  into  lbs. 

per  sq.  inch, 503 
Kilogrammetres    into   foot-pounds, 

506 
Kilometres  into  sea  miles,  497 

ii  into  >t  it  ate  miles,  497 

Kirk's  analysis.  93  97 
Knees,  beam,  296, 297,  299 
»      bracket,  297 

Laburnum.  475 
Lacing  pieces.  52 
Lance  wood,  475 
Landings,  312 
I.  a  rob,  475 
Lashing  rings,  305 
Launching,  99,  104 
Launching  curves,  99, 101 
data, 102,  103 
44  periods,  99 

L.W.L.,  area  of,  8,  45,  47,  48,  54 
Lead,  cast,  475 

"      sheet.  47" 
Least  radius  of  gyration  of  various 

sections,  208, 209, 819 
Ledges,  hatch,  305 
Life-boats,  427,  441,443 
Life-preservers,  432,  438,  445 
-Lifting  rings,  305 
Light  screens,  451 
Lignum  vita-,  475 
Lime,  475 
Limestone,  475 

Lime  w 1,  476 

Liners,  bulkhead,  308 

11      at  overlaps,  312 
Liners,  294 
Linoleum,  476 

Litres  into  CT.S.  gallons,  499 
Lloyd's  equipment  rule,  412 
"      riveting  table,  260,  261 
"      rudder  formula,  106 
L.  M.  C.  by  Tchibyschetf'srule,28,29 
Load-draught  diagrams,  90,  91,  92 
Load-line  half-breadths,  53 

"         diagram,  56 
Logarithms  of  numbers,  552,  577 

"  of  important  numbers, 

577 
Longitudinals,  307 
Longitudinal  metacentre,  16,17,28, 

29,31,34,35 
"Lucania,"    Tchibyscheff    sections 
for,  23 


Luff-tackle  purchase,  400 

Ti  a  ho-  a  .i  >  .  476 

Manholes  in  inner  bottoms,  294 
Mantissa  of  logarithm,  553 
Maple,  476 

Marble,  476  Mi 

Margin  plate  in  tanks,  292,  293,  294 
Marine  engines,  elements  of,  60,  61 
Marline,  392 

Mathematical  tables,  493-5.  < 
Metacentre,  transverse,  13,  30,  33,^6, 
37, 45  r 

"  longitudinal, ,16,  17,28, 

29,31,34,36 
Metres,  into  feet,  496 

"        into  yards,  500 
Metric  system,  495-507 

"       tons  into  tons,  504 
Mica,  476 

Midship  section  area,  10 
Mid.  area  coefficient  /3,  10,  45,  47,  48 
Millimetre,  495,  496 
Modulus  of  elasticity,  204 
Moment  of  inertia,  205,  208,  209,  211, 
212,  215,  216 
»         of  inertia  of  circular  sec- 
tions, 216,  217 
"        of  inertia  of  waterline  co- 
efficients, 49 
«        of  inertiaof  water  plane,  14 

Moment  of  resistance,  206,  208,  209, 
211,  213,  215,  216 
"        to  alter  trim  one  inch,  19 
"         to  change  trim,  17 

Monkey  forecastle,  77 

Mooring  anchors,  418 

Mortar,  476  ■ 

M  ultipliers  for  subdivided  intervals, 

"  for  Tchibvscheff's  rule, 

22 
Mushroom  mooring  anchors,  418 
Muntz  metal,  476 


f  u  n  c- 


]¥atural  sines,  508-512 

ii  trigonometrical 

t ions,  508-512 

Nautical  mile,  488 

Neutral  surface,  205,  206 

New  York  Yacht  Club  racing  rules, 

466-472 
Nickel,  476 
Nitric  acid,  476 
Norman  head,  279 
Notes  on  wire  rope,  232,  233 
Numbers,  logarithms  of,  552-5.7 

ii  powers  and  roots  of,  521- 

5.-.1 
Nuts,  U.  S.  standard,  336,  337 


584 


Index 


Oak,  476 

"  Oceanic,"  body  plan  of,  57 
Oil,  linseed,  476 

"    olive,  476 

"    petroleum,  476,  479 

"    whale,  476 

Openings,  tonnage,  87,  88 
""•  Ordered  lengths  of  rivets,  269 

W    Ore,  red  iron,  476 

"    brown,  476 

"    Clydesdale,  476 
Oregon  pine,  476 
Ounces  Into  grammes,  505 
Oxter,  fairing  the,  62 

it,  513 

Pad-eyes,  standard,  356,  357 
Paper,  building,  476 
Parcelling  and  serving,  388 
Parson's  turbines,  60 
Pens,  cattle,  111 

"      sheep,  112 
Permanent  set,  205 
Petroleum,  refined,  476 
"  Texas,  476 

Pewter,  477 
Phosphor  bronze,  476 
Physical  properties  of  timber  228-231 
Pillar  heads  and  heels,  302 
Pillars,  hold,  301,  302,  303 

pipe,  221-226,  302,  303 
Pins,  belay,  331 

"      moments  on,  246,  247 

"     standard  toggle,  373 
Pine,  Georgia,  477 
Pintles,  278,  280,  285 
Pipe,  221-226,  302,  303 
Pitch,  476 

"        pine,  477 
Plate  lines,  309 
Plating,  shell,  308-313 
Platinum,  477 
Plough  steel,  379 
Plug  cock,  Keys,  358 
Plumbago,  477 
Poop,  77 
Poplar,  477 

Pounds    per    sq.  inch   into  atmos- 
pheric pressure,  503 
"  per    sq.    inch    into    kilo- 

grammes per  sq.  cm.,  503 
"  into  kilogrammes,  504 

Powers  and  roots  of  numbers,  521- 

551 
Pressed  plate  chocks,  289 
Pressure  on  dog-shores,  104 

"         of  water  at  various  heads, 
485 
Prismatic  coefficient,  10,  45,  47,  48 
Proof  load  for  chains,  234 

*'     of  Simpson's  rule,  3 


Proof  of  strength,  203 

Propeller  brackets,  area  of,  109,  110, 
286 
"  struts,   108,   109,    110,  286, 

287 
"  struts,  Simpson's  formula 

for, 108 

Proportions  of  chain  slips,  370 
of  towing  bitts,  368 
of  ventilating  cowls,  377 
of  ship's  bells,  330 


Quartz,  477 

Radius  of  gyration,  206,  208,  209, 

215,  216,  218,  219 
Rail  half-breadths,  53 
Raised  quarter  deck,  78 
Range  lights,  451 
Ratlines,  388 
Reels,  length  of,  392 
Regulations,  Board  of  Trade,  428-439 
"  Department    of     agri- 

culture, 111 
"  United  States  inspec- 

tion, 440-460 
Relation  coefficient,  45,  47,  48 

"        of  the  coefficients  to  one 
"  another,  47 

Resilience,  204 
Resistance  of  framing,  288 

"  moment  of,  206,  208-216 

"  of  sbips,  186-199 

"  form  of  least,  195-199 

"         skin,  188-190,  195 
"  wave-making,  188-190, 195 

Reverse  frames,  289,  290 
Rigging,  derrick,  406,  407 
"        and  ropes,  379-407 
"        standing,  379 
"        chain,  398 
"        ropes,  382,  383 
"        screws,  374,  375 
Rings,  lifting.  305 
Ring  plates,  360 
Rings,  wrought  iron,  359 
Riveting  of  boss,  278 
Riveting,  U.  S.  Navy  standard,  252- 

259 
Riveting,  Lloyd's,  260, 261 

"        strength  of,  266-271 
Rivets,  standard,  259,  263 
Roots  and  powers  of  numbers,  521- 

551 
Ropes,  389 
Rope,  coir,  389,  392 
"      hemp,  389,  391 
"     manila,  389,  390 
"      small  stuff,  392 
"      cotton,  392 
"      wire,  379 


Ind 


ex 


585 


Rope-end  fittings,  387.  388 
Ropes,  rigging  and,  379-4n7 
Round  bar,  weight  of,  151,  162 
Round  of  beam  (freeboard*,  76 
Rodder,  area,  106.  107,  106        I  0  0T~ 
arms,  279 
balanced.  106,  281 

-t  steel,  280 
coupling  bolts,  279.  285 
44       coupling  palm.  279,  280,  285 

carrier-.  §82,  283,  284 
"        emergency  chains,  280 
"       heel  bearing.  280 
tail  plat.-, 
trunks,  286 
"        post,  278 

stock,  106,  107. 109. 279 
Rule  for  moment  t>>  alter  trim.  19 
"     for  moment  to  change  trim.  17. 

18 
'•     for  ordering  rivets.  269 
*'     for  pressure  on  dog  shores.  104 
"     for  pressure  on  rudder.  105 
"     for  prismatic  coefficient.  10.  45 
"     for    propeller    struts,    (Simp- 
son's), 109 
"    for  radius  of  gvration,  206,  208, 

209  215,  218 
"     for  racing  vachts,  <  N.  Y.  Y.  C), 

466-472 
■•     for  relation  coefficient.  45 
•'     for  riveting  (Lloyd's),  260,  261 
•■     for  row  boats.  420 
"    for  rudder  area,  105 
•     for  rudder  stocks,  105-108 
"     for  sail  area,  422 
'•     for  sea  anchors,  362,  445 
44    for  size  of  blocks,  394 
44    for  shackles,  249,  250 
44     for  spectacle  frames,  110 
"     for  speed  ami  power,  187,  190, 

191,  192.  193.  194.  195 
44    for  strength  of  hemp,  391 
44     for  strength  of  manila.  403 
44     for  steamships  <Briti>h  .428-439 
"     for     steamships     (American), 

440-460 
41    for  stresses  on  anchor  cranes, 

325,  326.  327 
44    for  tackles,  401, 402  • 

"    TchibyBchefTs,  21.  2.V41 
14     for  tons  per  inch,  8 
44    for  twisting  moments  on  rud- 
ders, 106 
44     for  w»-tted  surface.  97.  98 
44     for  area  of  water  plane,  7 
44     for  B.  If.,  16,  45 
44    for      bending       moment-     on 

beams.  211,  213 
44    for  bending  moments  on  pins, 
246 


it 
>i 


.1 
ii 
ii 


Rule  for  bilge  diagonal  coefficient,  47 
•     for  bollards,  333 
14    for  bottom  breadth,  6 
••     for  C.  B.,  11.  12,  45 
"     for  centre  of  gravity.  175.  176 
"     for    centre    of   gravity   coeffi- 
cient, 45,  48 
44    for  centre  of  pressure  on  rud- 
ders, 105 
44     for  chain  cable  links,  417 
••     for  catting  hooks,  340 
44    for  columns  (Johnson's),  217, 

221 
44    for  crane  hooks,  339       ■ 
44    for  davits,  341 
44    for  end  links  on  cables,  417 
44    for  fairleads  or  chocks,  347 
for  finished  .-teel  weight,  115 
for  freeing  port  area,  76 
for  hawse  pipes,  354 
for  inertia  coefficient,  17,  45 
for  iron  rings,  359 
for    Johnson's  for  steel    col- 
umns. 217,  221 
for  Johnson's  for  steel  weights, 

115 
forL.B.M.,17 
for  L.  C.  B.,  12 
for  L.  M.  C.,  16 
44    for    maximum    bending    mo- 
ment on  hull.  1S5 
••     for  mid.  area,  10 

*alt.  477 

Sand.  477 
Sandstone,  477 
Satinwood,  477 

Scantlings  for  small  boats,  424,  425 
Scarphing  of  landing  edges,  312 

44  of  keels,  277 

Screens,  light,  451 
Screws,  dimensions  of  wood,  361 

44  rigging,  374,  375 

Sea  anchors,  areas  of,  362 

44    anchors,  detail  of,  363 
Sea  miles  into  kilometers.  497 
Section  modulus,  206,  215.  216 
Sellers'    standard    bolts    and    nuts, 

336,337 
Serving  twine,  392 
Shackles  for  blocks,  394 
Shackles.  lashing,  395 
44     special,  249-251 
44     standard.  366 
44     trade,  364,  365 
Shade  deck  vessel.  78 
Shearing    and    hearing    values    for 
river-.  272,  273 
44  st res-,  204 

Sheaves,  380.  3-1 

for  blocks,  393,  394.  398 


586 


Ind 


ex 


Sheep  pens,  112 
Sheer,  50,  75 

"       for  boats,  420 
44       for  freeboard,  75 
"       poles,  388 

"       strake,  308,  310,  312,  313 
Shell  plating,  308-313 
"      plate  lines,  309 
"      riveting,  312 
Shift  of  butts,  310 
Shingle,  477 
Ship's  bells,  330,  331 
Sboe  for  wire  rope,  387,  388 
Side  girders  in  tanks,  292 
Side-lights,  weights  of  brass  framed, 

369 
Side  stringers,  306,  310 
Signs,  algebraical,  ix 
Silver,  477 
Simpson's  first  rule,  1 

"  formula  for  struts,  108 

Single  plate  rudders,  279 
Size  of  hatches,  303 
Slate,  477 

Slips,  proportions  of  chain,  370 
Snatch  blocks,  393 
Snow,  477 
Space,  crew,  466 
Spanish  Burton,  400,  401 
Spar  deck  vessel,  78,  81,  85 
Spars  for  small  boats,  420 
Specification  headings,  64-72 
Specifications,   the  preparation  of, 

64 
Spectacle  frames,  110,  287 
Speed  and  power,  186,  187 
Speed  tables,  488-492 
Spirketting  plate,  289,  290 
Splices,  380,  381 

"        allowances  for,  383 
Spruce,  477 
Square  bar,  weight  of,  151,  152 

"  centimetres  into  square 

inches,  498 
"  foot   into  kilogrammes 

per  sq.  metre,  502 
"  inches  into  square  cen- 

timetres, 498 
"  kilometres  into  square 

miles,  501 
"  metres       into      square 

yards,  500 
"  metres  into  pounds  per 

sq.  foot,  502 
"  miles  into  square  kilo- 

metres, 501 
"  yards    into    square  me- 

tres, 500 
Squares  of  numbers,  521-551 
Square  roots  of  numbers,  521-551 
Stability  calculation,  38,  43 


Stability  curves,  43 

Staggered  pillars,  303 

Stalls,  cattle,  111,  112 
horse,  112 

Standard  pipe  elements,  223,  224 

Standard  rivets,  259,  263 
"  shackles,  366 

"  thimbles,  385,  386 

"  toggle  pins,  373 

"  ventilator  cowls,  376,  377 

Stapled  collars,  289 

Statute  miles  into  kilometres,  497 

Statutory  deck  line,  89 

Stealers,  309 

Steamers'  data,  200,  201 

Steel,  weights  of,  120-170,  477 

Steel,  plough,  379 

Steel  wire  ropes,  379,  382,  383 

Steering  gear  hood,  77 

Stems,  277,  278 

Stem,  contour  of,  51 
"       scarph  of,  277 

Stern  frames,  278,  279 

Strakes,  arrangement  of,  309 

Strength  of  chain  cables,  234 
"         of  columns,  218 
"         of  guard  chains,  235 
"         of  materials,  203-273 
"         of  metals  and  alloys,  226, 

227 
"         of  special  shackles,  249-251 
"         of  tackles,  401, 402,  403,  404, 
405,  406 

Strength  of  timber,  230,  231 

Stress  and  strain,  203,  204 

Stresses  on  floors,  290 

Strong  beams,  299 

Strops  for  blocks,  395 

Structural  details,  275-313 

Stuffing  boxes  and  glands,  371 

Swivel  jaws,  395 

Sycamore,  477 

Symbols,  vii 

Table  of  logarithms  of  numbers, 
552-577 

"         of  powers  and  roots, 521-551 
Tables  of  strength  of  riveting,  266- 

271 
Tack»rivets  in  keels,  275 
Tackles,  399-407 
Tackle,  gun,  400 

"        luff,  400 
Tackles,  relieving,  401 

"  strength  of,  404,  405 

Tail  plates,  286 
Talc,  477 
Tallow,  477 
Tanks,  circular,  484 

"       rectangular,  482,  483 
Tank  bleeders,  294,  295 


Index 


587 


Tar,  477 

Tehibyscheff's  rule,  22 
Tehibyseheff's  sections,  39 

sections  for    "  Luca- 
niii,"  23 
Teak,  Burmese,  477 
Tee  Bteel,  weight  of,  125-129 
Tees  as  struts,  248 
Tensile  stress.  204 
Thames  measurement  tonnage,  472 
Thermal  units  into  calories,  607 
Thimbles  for  wire  rope,  372,  380,  384, 

385,386 
Threefold  purchase,  400 
Tile,  477 
Tiling.  477 
Tin,  477 

Toggle  pins,  373 
Tons  into  metric  tons,  504 
Tonnes-metres  into  foot-tons,  507 
Tonnage,  401-165 

B.  O.  M..  472 
"  openings,  87,  88 

•'  Thames  measurement.  472 

"         schedule,  462,  463 
Tons  per  inch  immersion,  8 
I . >j.gallant  forecastle,  77.  78 
Topping  lifts,  402,  406,  407 
Torsional  stress,  204 
Towing  bitts,  368 

Transverse  metaeentre,  13,  30,33,  36, 
37,45 
44         metaeentre,    by    Tchib- 
vscheff's  rule,  30 
Trap.  477 

Trial  trip  tables,  488-4'J2 
Trigonometrical  functions,  natural, 

508-512 
Trim,  alteration  to,  20 

M      moment    to    alter    one    inch, 

19 
44     moment  to  change,  17 
Trunk  deck  vessel,  78 
Tube-end  eastings,  287,  288 
Turbines.  Parson's  marine,  60 
Turnbuckles,  388 

Admiralty,  375 
Turret  deck  vessel,  78 
Twine,  serving,  392 
Tvpes   of  rudder   carriers,  282,  283, 
284 
44     of  vessels  (freeboard),  77,  78 

Ultimate  strength,  203 

United  States  department  of  Agri- 
culture, 111 
U.  S.  gallons  into  litres.  499 
U.  S.  inspection  laws,  440  400 
U.  S.  standard  bolts   and   nuts,  33G, 

337 
Universal  bar,  - 


Values  for  Johnson's  formula,  220 
Various  stresses  and  their  factors, 
207 

Ventilator  cowls,  376,  377 
Ventilation  flanges,  350 
Ventilators,  cattle,  112 

Walnut.  477 
Water,  477,  478 
Water  notes,  486 
Water  plane,  area  of,  7 
Watertight  compartments,  292,  307 
44  doors,  details  of,  345 

44  doors,  hinged,  344 

44  doors,  sizes  of,  342 

44  doors,  sliding,  343 

44  floors,  291 

Ways,  length  of,  102 
Web  frames,  305,  306 
Wedges,  hatch,  305 
Weight  of  Acacia,  473 
41        of  alder,  473 
44        of  aluminium,  473 
44        of  anchors,  319,  321,  323,  418 

of  angle  steel,  120-124 
44        of  antimony,  473 
44        of  anthracite  coal,  473 
44        of  ash,  473 
44        of  asphalte,  473 
41        of  asbestos  board,  473 

of  Babbit  metal,  473 
44        of  bars,  120-170 

of  bells,  331 
44        of  bitts,  333,  368 

of  blocks,  396,  397 
44        of  boats,  341 

of  bollards,  333 
44        of  bolts,  481 
of  brick,  473 
44       of  brass,  473 
44        of  bronze,  473 
44        of  bulb-angle,  155-160 
44        of  bulb-plate,  161,  162 
44        of  bulb-tee,  163-170 
44        of  cables,  236 
44        of  camphor,  473 
44        of  canvas,  478 
44        of  cement,  474 
44        of  chain,  236,  398 
44        of  coal,  474 
44        of  copper,  474 
44        of  cowl  ventilators,  376 
44        of  deals,  Riga,  474 
44        of  elm,  474 

of  fir,  474 
44        of  glass,  475 
44        of  greenheart.  475 
44         of  gunmetal,  47". 
of  hemlock,  475 
44         of  hemp  rope,  391 
44        of  India  rubber,  475 


588 


Index 


VTeigl 

it  of  iron,  475 

Weight  of  thimbles,  381 

(t 

of  larch,  475 

"       of  tiling,  inlaid  rubber,  477 

it 

of  lead, 475 

"       of  tiling,  vitrified  brick,  477 

ii 

of  lignum-vitoe,  475 

"       of  tiling,  white,  477 

11 

of  lime,  475 

"       of  timber,  231,  473-478 

ii 

of  linoleum,  476 

"       of  tin,  477 

ii 

of  mahogany,  476 

"       of  walnut,  477 

ii 

of  manila  rope,  390 

"       of  water,  478,  486 

ii 

of  maple,  476 

*'       of  white  pine,  478 

ii 

of  Muntz-metal,  476 

"       of  yew,  478 

ii 

of  nickel,  476 

"      of  zee  bars,  130-134 

ti 

of  oak, 476 

"       of  zinc,  478 

ti 

of  oil,  476 

Welded  beam  knees,  296,  297,  299 

ii 

of  ore,  476 

Well-decked  vessel,  77,  78 

>i 

of  Oregon  pine,  476 

Wetted  surface  formula,  97,  98 

ii 

of  paper,  476 

Wheat,  478 

ii 

of  petroleum,  476 

Wheels,  standard  hand,  351,  352 

ii 

of  phosphor  bronze,  476 

Whip,  399 

ii 

of  pine,  477 

Whip-upon-whip,  399 

ii 

of  pitch,  476 

White  metal,  478 

ti 

of  pitch  pine,  477 

"      pine,  478 

tt 

of  poplar,  477 

Whitworth  bolts  and  nuts,  480 

tt 

of  rope,  390,391,392 

Willow,  478 

tt 

of  rope  wire,  232,  382,  383 

Wire  ropes,  flexible  steel,  382,  383 

it 

of  round  bar,  151,  152 

Wire  rope,  end  fittings  for,  387 

tt 

of  sand,  477 

"    rope,  thimbles  for,  372 

t« 

of  satinwood,  477 

"     rope,  notes  on,  232,  233 

tt 

of  shapes,  120-170 

Worked  eyes,  standard,  367 

it 

of  sheaves,  381 

Working  load,  203 

ii 

of  sheet  steel,  154 

Wrecking  blocks,  394 

tt 

of  sidelights,  369 

tt 

of  spruce,  477 

Yacht's  launches,  426 

it 

of  steel,  120-170 

Yacht  racing  rules,  466^172 

tt 

of  square  bar,  151,  152 

Yards  into  metres,  500 

tt 

of  tallow,  477 

Yew,  478 

ii 

of  tar,  477 

<t 

of  teak,  477 

Zee  bar,  weight  of,  130-134 

it 

of  tee  bar,  125-129 

Zinc,  478 

ii 

of  tee  bulb,  163-170 

C_"S^ 


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